CHANGELOG.md

Changelog

[unreleased]

• #382:

  • Makes the name argument to sicmutils.operator/make-operator optional. name now defaults to '???.

  • adds tests for all code forms in Chapter 8 of FDG.

• #376 adds more type hints to the ratio.cljc namespace. This fully solves the advanced compilation issues we were seeing.

• #374: Demos, thanks to @sigmaxipi!

• #379 fixes typos in a couple of the equations in richardson.cljc, closing #377. Thanks to @leifp for the report.

• Features, tests and bugfixes from #381:

  • sicmutils.calculus.coordinate/generate moves to sicmutils.calculus.manifold/c:generate; this supports a bugfix where 1-dimensional manifolds like R1-rect, aka the-real-line, return a coordinate prototype of a single element like t instead of a structure with a single entry, like (up t). Thanks to @phasetr for the bug report that led to this fix, and @gjs for finding and fixing the bug.

  • same.ish/Approximate implemented for sicmutils.structure/Structure, allowing ish? comparison of up and down structures with approximate entries. Require sicmutils.generator for this feature. (NOTE: because protocols are implemented for the LEFT argument, (ish? <vector> (down ...)) will still return true if the values are approximately equal, even though a <vector> is technically an up and should NOT equal a down. Do an explicit conversion to up using sicmutils.structure/vector->up if this distinction is important.)

  • same.ish/Approximate now defers to sicmutils.value/= for equality between Symbol and other types. This lets ish? handle equality between symbols like 'x and literal expressions that happen to wrap a single symbol.

  • Cartan->Cartan-over-map now does NOT compose (differential map) with its internal Cartan forms. This fixed a bug in a code listing in section 7.3 of FDG.

  • Section 7.3 of FDG implemented as tests in sicmutils.fdg.ch7-test.

  • Many new tests and explorations ported over from covariant-derivative.scm. These live in sicmutils.calculus.covariant-test.

  • timeout exceptions resulting from full GCD are now caught in tests using sicmutils.simplify/hermetic-simplify-fixture. Previously, setting a low timeout where simplification failed would catch and move on in normal work, but fail in tests where fixtures were applied.

0.19.2

Yet another incremental release, this time to bump the Fraction.js dependency. The new cljsjs dependency has code compatible with advanced compilation.

• #372 bumps the Fraction.js dependency to 4.1.1.

0.19.1

This is an incremental bugfix release to get Clojurescript advanced compilation into shape.

• #371:

  • fixes a subtle bug with extern inference on fraction.js/bigfraction.js. Thanks to @sigmaxipi for this report!

  • removes overridden factory constructors like ->Polynomial. I had originally done this for functions that held a metadata field, so that the user could leave it out and have it default to nil... but advanced Closure compilation can't understand the ns-unmap call, so it has to go.

  • Many unary functions on Operator, Structure, Series, PowerSeries, Polynomial and RationalFunction now preserve metadata. Binary functions between two instances of any of these still return a new object with metadata == nil.

0.19.0

(If you have any questions about how to use any of the following, please ask us at our Github Discussions page!)

This release focused on improving the expressiveness and performance of the three simplification engines in SICMUtils:

• sicmutils.polynomial and sicmutils.rational-function are now quite well fleshed out, with full polynomial and rational function APIs and many generics.

• The polynomial and rational function simplifiers work by round-tripping expressions through these types, depending on each namespace to emit symbolic expressions in "canonical form". This process is now much faster! On one important Bianchi Identity benchmark in sicmutils.fdg.bianchi-test, one test that formerly took close to 30 minutes now runs in 30 seconds, and all see a 60-fold improvement.

• By default, these simplifiers emit expressions with all terms multiplied out; the new factor function in sicmutils.env lets you factor expressions, overriding this default.

• The rule-based simplifier is now based on a powerful pattern matching engine, implemented in pattern.match and pattern.rule. sicmutils.simplify.rules now contains every rule and possible customization from the original scmutils codebase.

There is a lot in this release, all motivated by performance. Please read on for the detailed notes, and enjoy version 0.19.0!

Rule-Based Simplifier Overhaul

• #353 introduces a powerful new simplifier, ported from the new-simplify procedure in simplify/rules.scm of the scmutils library. There are now a BUNCH of new rulesets and rule simplifiers in sicmutils.simplify.rules!

  The next step with these is to massage them into separate bundles of rules that users can mix and match into custom simplifiers for objects like abstract matrices, abstract bra and ket structures, up and down, booleans (for representing equations and inequalities) and so on.

• #349 introduces a new pattern matching system, built out of matcher combinators. All of the rules in sicmutils.simplify.rules now use the new syntax offered by the library. Some notes:

  • pattern.match defines a number of "matcher combinators"; these are functions that take a map of bindings, a data input and a success continuation and either succeed by calling their continuation, or fail. Out of the box, the library provides fail, pass, with-frame, update-frame, predicate, frame-predicate, eq, bind, match-when, match-if, or, and, not, segment and sequence.

  • Additionally, any combinator that takes another combinator can ALSO take a pattern form like '?x. See pattern.syntax for the full, rich range of syntax allowed. These are all functions, so you'll have to quote your symbols at this stage.

  • Passing a matcher combinator to pattern.match/matcher to generate a matcher object. This is a function from some data input to a map of bindings on success, or an explicit pattern.match/failure object on failure. Test for failure with pattern.match/failed?.

  • A combination of a matcher and a "consequence function" is called a "rule". A consequence is a function that takes a binding map and either returns a new result or fails by returning nil or false. (Don't worry, you can succeed with these values too by wrapping them in sicmutils.rule/succeed.)

    Rules are the heart of the whole simplification mechanism in sicmutils! To learn about how to build these, see the documentation for pattern*, pattern, consequence, template, rule*and rule.

  • pattern.rule gives you some starter rules, and many combinators you can use to build more and more powerful and complex sets of rules. These are pass, fail, predicate, return, branch, choice*, choice, pipe*, pipe, n-times, attempt, guard, iterated, while, until, fixed-point and trace.

  • Rules are nice for rewriting entire expressions recursively, from the bottom up or top down. This is called "term rewriting". A big motivation for this rewrite was to make it easy to build custom term rewriters for types like abstract matrices or abstract up and down structures. You can use your rules to rewrite structures recursively with bottom-up, top-down, iterated-bottom-up and iterated-top-down. ruleset*, ruleset, rule-simplifier and term-rewriting capture some common patterns the library uses to go from rules => term rewriters.

  • If you want ideas about how to use the pattern matching library to rewrite expressions, see sicmutils.simplify.rules for many examples.

• #354 adds SCI support for all macros and functions in the new pattern matching namespaces, and adds these to the namespaces exposed via sicmutils.env.sci.

Rational Function, Polynomial Simplifiers

• #341 takes on a large rewrite of the rational function and polynomial simplfiers. One goal of this project was to improve the performance of the Bianchi Identities in sicmutils.fdg.bianchi-test, and I'm happy to say that they are now a good bit faster than the original scmutils implementation.

  sicmutils.polynomial and sicmutils.rational-function are now solid data structures of their own, with many operations installed into the generic system. These are now valuable and useful outside of their role in the simplifier.

  This was a large project, and many small improvements and bugfixes snuck in. Here is the full list:

  • v/kind now works for sorted-map instances.

  • GCD in Clojurescript is now fast and efficient between all combinations of js/BigInt and js/Number, and in Clojure between all combinations of clojure.lang.BigInt, BigInteger, Long and Integer.

  • on the JVM, GCD now works properly with rational numbers. Previously anything non-integral would return 1; now (gcd 1/2 1/3) properly returns 1/6.

  • g/exact-divide now succeeds for all non-exact ::v/scalar types (symbols, floats, etc) either if the denominator is zero, or if the two arguments are equal. Else, it throws, just like before.

  • A multi-arity call to sicmutils.generic/* now stops if it encounters a 0, rather than attempting to multiply all remaining items by 0.

  • The default function for sicmutils.generic/lcm protects against overflow by dividing only a single one of its arguments a and b by (gcd a b).

  • (g/lcm 0 0) now properly returns 0.

  • New sicmutils.util.aggregate/{monoid,group} functions let you build multi-arity aggregations out of binary combination functions, with an option to bail early at "annihilator" values, like 0 for multiplication.

  • New multi-arity lcm and gcd implementations for symbolic expressions appropriately handle 0 and 1 on either side, as well as the case where both arguments are equal.

  • In the sicmutils.numsymb namespace, thanks to monoid and group, the '*, '/, '-, '+, 'or, 'and, 'gcd, 'lcm and '= operations now have efficient multi-arity implementations that stop computing when they receive an annihilator, like 0 for multiplication or true for or. Access these via (sicmutils.numsymb/symbolic-operator <symbol>).

  • sicmutils.series/PowerSeries gains arg-scale and arg-shift functions; these are identical to sicmutils.function/arg-{scale,shift}, but preserve the PowerSeries type. (#367 proposes making these functions generic.)

  • New sicmutils.ratio/IRational protocol, with numerator and denominator functions implemented for ratios and for the RationalFunction data type. These two are now exposed in sicmutils.env.

  • sicmutils.simplify.rules/*divide-numbers-through-simplify?* is now true by default; numbers in the denominator will now automatically pull up into the numerator. All tests now reflect this setting.

  • Any analyzer generated from sicmutils.expression.analyze can now act on both bare, unwrapped expressions (raw lists etc) and on sicmutils.expression.Literal instances. This means that you can now call sicmutils.simplify/{*rf-simplify*,*poly-simplify*} as functions and canonicalize some form with either simplifier without triggering a full simplification. A small win, but ice.

  • sicmutils.polynomial.factor got a major rewrite, and now exposes a few functions like poly->factored-expression, factor-expression and factor.

    • factor is tremendously useful! Call factor (it's aliased into sicmutils.env) on any expression to factor out all possible terms. This makes it much easier to see where there is some cancellation lurking, in, say, some expression you know should equal zero (a residual).

  • bugfix: sicmutils.expression.Literal instances now compare their contained expression via sicmutils.value/=.

  • sicmutils.rules/constant-elimination can now eliminate constants from expressions with any arity, not just binary forms.

  Now, the three big namespaces... sicmutils.polynomial, sicmutils.rational-function and sicmutils.polynomial.gcd all got a big overhaul.

  • sicmutils.polynomial notes:

    • Polynomial uses a new sparse representation for its "power product" term; this, plus an arithmetic rewrite, makes the whole system much faster for larger numbers of variables (for all #s, really).

    • Polynomial instances implement many more Clojure(script) protocols. They can hold metadata; they can be evaluated as functions of their indeterminates, and seq now returns a sequence of terms.

    • Polynomial extends sicmutils.function/IArity and differential/IPerturbed, so you can use sicmutils.function/arity, and take derivatives of functions that return polynomials.

    • In their arithmetic, Polynomial instances will drop down to bare coefficients whenever some multiplication or addition removes all indeterminates. All binary arithmetic exposed in the namespace can handle non-Polynomial instances on either or both sides, so this is fine. Coefficients are treated as constant polynomials.

    • The namespace holds many new functions. Some choice ones are:

      • constructors: make, constant, linear, c*xn, identity, and new-variables

      • accessor functions: arity, degree, coefficients, leading-term, leading-coefficient, leading-exponents, leading-base-coefficient, trailing-coefficient, lowest-degree

      • predicates: monomial?, monic?, univariate?, multivariate?, negative?

      • functions to generate new polynomials: map-coefficients, map-exponents, scale, scale-l, normalize, reciprocal, drop-leading-term, contract and extend alongside contractible?, lower-arity, raise-arity, with-lower-arity, arg-scale, arg-shift

      • arithmetic: negate, abs, add, sub, mul, square, cube, expt, divide along with divisible?, evenly-divide, pseudo-remainder, and lots of functions installed into the generic arithmetic system.

      • different ways to evaluate polynomials: evaluate, horner-with-error

      • calculus! partial-derivative and partial-derivatives are alive and well, and work with the D operator.

      • Functions to get in and out of polynomials from other types: univariate->dense, ->power-series, expression->, ->expression

  • sicmutils.polynomial.gcd also got a rewrite; it's fairly clear to read now, and prepared for the eventual addition of the sparse multivariate GCD routine that scmutils uses. There are some efficiency gains here too that let us turn a number of tests back on, or demote them from :long markers.

  • sicmutils.rational-function notes:

    • RationalFunction instances implement many more Clojure(script) protocols. They can hold metadata; they can be evaluated as functions of their indeterminates, and seq now returns a pair of numerator, denominator.

    • RationalFunction extends sicmutils.function/IArity and sicmutils.ratio/IRational, so our generic arity, numerator and denominator work on these instances.

    • Here are some new functions from the RationalFunction namespace:

      • constructor: make, drops to polynomial or coefficient where needed just like Polynomial functions

      • functions to generate new rational functions: arg-scale, arg-shift

      • predicates: negative?

      • arithmetic: negate, abs, add, sub, mul, square, cube, expt, invert, div, gcd, and many functions installed into the generic arithmetic system.

      • evaluation via evaluate

      • calculus! partial-derivative and partial-derivatives are alive and well, and work with the D operator.

      • Functions to get in and out of rational functions from symbolic expressions: expression->, ->expression.

New Functions, Performance Improvements

• #358:

  • Adds a more efficient literal-derivative implementation to sicmutils.abstract.function, making the Bianchi identity benchmarks run 40% faster.

  • In Clojurescript, Range instances now implement sicmutils.value.Value and sicmutils.differential.IPerturbed, allowing them to be returned from derivative-taking functions

  • Major, unexpected performance improvement - it turns out sicmutils.value/number? was quite slow in Clojure (less so in Clojurescript). Changing this function from an isa? check to a series of explicit instance? checks cut the build time in half. This makes the numeric tower less extensible... but it wasn't terribly extensible to start with, and needs some attention to make it so. A big win!

  • The Bianchi identity benchmarks have all been updated to reflect the big performance improvements achieved here, thanks to the wonderful Tufte profiling library from @ptaoussanis. The remaining very slow piece in the simplifier is the implementation of g/add for polynomial instances. #341 will improve this situation.

• #360 introduces a number of performance improvements to the sicmutils.differential.Differential implementation, primarily in terms:+ and terms:*. thanks again to @ptaoussanis and the Tufte profiling library for helping me track these down.

• #357:

  • Adds the ability to do incremental simplification, every time an operation is performed involving a symbolic expression. Bind sicmutils.numsymb/*incremental-simplifier* to a function from raw expression -> raw expression, like sicmutils.simplify/simplify-expression or any of the rules in sicmutils.simplify.rules to enable this behavior.

  • Expands the sicmutils.expression.analyze API with the functions default-simplifier, expression-simplifier, initializer, expression-analyzer and auxiliary-variable-fetcher. See the API documentation for detailed notes on how to do interactive expression analysis and simplification with these new tools.

  • by default, each simplification pass uses both rational function and polynomial canonicalization. This brings the simplifier into line with the scmutils simplifier.

• #353:

  • Adds a new sicmutils.util.logic namespace with an assume! function that allows rules to log assumptions when some simplification like (sqrt (square x)) might have to choose one of multiple possible simplifications ((non-negative? x), in this example).

    This function simply logs the assumption for now, instead of performing any checks. now. Turn off assumption logging with the dynamic variable *log-assumptions?* in that namespace.

  • new sicmutils.value/almost-integral? returns true if its argument is VERY close to an integral value, false otherwise.

• Efficient symmetric-difference implementation in sicmutils.util.vector-set (#346)

Bug fixes, file moves, misc

• #369:

  • Removes JVM dependencies on Guava and nrepl.

  • Removes sicmutils.env/sicmutils-repl-init; this is only used by lein repl, and we now accomplish the same task with the :repl-options entry in project.clj.

  • Makes sicmutils.polynomial.{factor,gcd} available to SCI via the sicmutils.env.sci namespace

  • moves a few namespaces to more valid locations, now that the rational function and polynomial namespaces are tidied:

    • sicmutils.numerical.interpolate.polynomial -> sicmutils.polynomial.interpolate

    • sicmutils.numerical.interpolate.richardson -> sicmutils.polynomial.richardson

    • sicmutils.numerical.interpolate.rational -> sicmutils.rational-function.interpolate

• #358:

  • Converts the Clojurescript test build and REPL command from lein-cljsbuild to shadow-cljs. This enables more formerly-slow tests for Clojurescript; these are now fast enough to run, thanks to the performance improvements described below.

  • Upgrades our Timbre logging dependency to version 5.1.2, and SCI to 0.2.5

• #353:

  • expression->stream, expression->string, print-expression, pe move from sicmutils.simplify to sicmutils.expression, and are now aliased in sicmutils.env.

  • pattern.rule/guard now fails if its rule argument fails; previously it wrapped the result in attempt, and would return its original input on failure.

  • fixed a heisenbug in sicmutils.expression.analyze/make-analyzer where, in Clojurescript, using expressions containing a js/BigInt as a hashmap key caused certain simplifications to fail. (This is vague, but the bug was really subtle.) The fix was to make sure we freeze keys in the symbol cache. This is now noted in the function body.

0.18.0

(If you have any questions about how to use any of the following, please ask us at our Github Discussions page!)

This release focused on porting over all of the material required to run every piece of code from Sussman and Wisdom's "Functional Differential Geometry". The namespaces are lightly documented; the situation is better than the original library, but will only get better as I work through the material and add commentary.

There is a huge amount of functionality and material here! We can run many examples from general and special relativity, and the tests are full of exercises from the classic "Gravitation" book by Misner, Thorne and Wheeler (MTW).

Notable changes from the rest of the library:

• Operator instances are slightly more efficient with their addition and multiplication, handling zero? and one? cases appropriately

• Structures can now hold metadata

• We've extended the SICMUtils generics to Clojure's Map and Set data structures. These can now combine with +. Maps are treated as sparse infinite-dimensional vector spaces, and can multiply with symbolic or numeric scalars.

• ModInt instances are now correctly equal to numbers (when those numbers mod down to the ModInt instance's residue).

What's next?

The next major change will be an overhaul of the simplifier to make it work fast enough to solve Einstein's field equations in a reasonable amount of time, maybe even in the browser. Polynomial GCD is slow, but #341 will make it fast.

On to the detailed notes!

Functional Differential Geometry

• From #339:

  • The new sicmutils.calculus.covariant/Lie-D can compute the Lie derivative for coordinates.

  • sicmutils.calculus.frame lets us create relativistic reference frames for investigating special relativity problems. This namespace aliases the following functions into sicmutils.env: 'frame?', make-event, event?, claim, coords->event, event->coords, ancestor-frame, frame-name, frame-owner and frame-maker.

  • sicmutils.calculus.hodge-star implements the Hodge star operator from chapter 10 of Functional Differential Geometry, plus Gram Schmidt orthonormalization. This namespace aliases the following functions into sicmutils.env: Gram-Schmidt, orthonormalize and Hodge-star.

  • sicmutils.calculus.indexed ports over the scmutils work on indexed objects and typed functions. This namespace aliases the following functions into sicmutils.env: argument-types, with-argument-types, index-types, with-index-types, typed->indexed, indexed->typed, typed->structure, structure->typed, i:outer-product and i:contract.

  • sicmutils.calculus.manifold gains coordinate-system?, which (predictably) returns true if its argument is a coordinate system, false otherwise. chart and point also take relativistic reference frames in addition to coordinate systems; the returned function converts to and from coordinates and events, rather than coordinates and manifold points.

  • Div, Grad, Curl and Lap move from sicmutils.calculus.derivative to sicmutils.calculus.vector-calculus. This namespace also contains versions of these operators from Functional Differential Geometry. This namespace aliases the following functions into sicmutils.env: divergence, curl, gradient and Laplacian (along with the others mentioned).

  • lots of new namespaces available in sicmutils.env.sci, soon to be deployed to Nextjournal: sicmutils.calculus.{hodge-star, indexed, vector-calculus}, and sicmutils.sr.{boost,frames}.

  • sicmutils.sr.boost describes boosts from special relativity, covered in chapter 11 of Functional Differential Geometry. This namespace aliases the following functions into sicmutils.env: make-four-tuple, four-tuple->ct, four-tuple->space, proper-time-interval, proper-space-interval, general-boost, general-boost2 and extended-rotation.

  • sicmutils.sr.frames implements relativistic reference frames from special relativity, covered in chapter 11 of Functional Differential Geometry. This namespace aliases the following functions into sicmutils.env: make-SR-coordinates, SR-coordinates?, SR-name, make-SR-frame, the-ether, boost-direction, v:c, coordinate-origin, add-v:cs and add-velocities.

• From #338:

  • sicmutils.fdg.bianchi-test verifies the Bianchi identities; this was a challenge posed by GJS, and getting it working exposed a few bugs and triggered the rest of the work in this PR. Thank you, GJS!

  • covariant-derivative now properly handles the case of functions with argument types attached.

  • added covariant-differential to sicmutils.calculus.covariant.

  • aliased all functions from various namespaces in sicmutils.calculus into sicmutils.env.

  • adds sicmutils.calculus.metric, with the following functions exposed in sicmutils.env:

    • coordinate-system->metric-components, coordinate-system->metric, coordinate-system->inverse-metric, literal-metric, components->metric, metric->components, metric->inverse-components, metric-over-map, lower, vector-field->oneform-field, drop1, raise, oneform-field->vector-field, raise1, drop2, raise2, trace2down, trace2up, sharpen, S2-metric

    • sicmutils.calculus.metric/invert is exposed as metric:invert to match the scmutils naming scheme.

  • adds sicmutils.calculus.connection, with the following functions exposed in sicmutils.env:

    • make-Christoffel-1, metric->Christoffel-1, metric->Christoffel-2, literal-Christoffel-1, literal-Christoffel-2, metric->connection-1, metric->connection-2, literal-Cartan, structure-constant

• #337:

  • adds sicmutils.calculus.curvature, with these new functions and many tests from the classic "Gravitation" book: Riemann-curvature, Riemann, Ricci, torsion-vector, torsion and curvature-components

  • form fields now have NO identity operator, since they multiply by wedge, not composition.

• #328 adds many utilities for "Functional Differential Geometry".

  • vector fields, in sicmutils.calculus.vector-field:

    • new functions: basis-components->vector-field, vector-field->basis-components

    • vector fields now implement v/zero? and v/zero-like by returning proper vector fields.

  • form fields, in sicmutils.calculus.vector-field:

    • new functions: nform-field?, basis-components->oneform-field, oneform-field->basis-components and function->oneform-field (aliased as differential-of-function)

    • Alt, alt-wedge provide alternate wedge product definitions

    • form fields now implement v/zero? and v/zero-like by returning proper form fields that retain their rank.

    • form fields now correctly multiply via * by using sicmutils.calculus.form-field/wedge, instead of composition.

  • maps between manifolds, in sicmutils.calculus.map:

    • new function: pushforward-function

    • differential becomes differential-of-map, aliased back as differential

  • sicmutils.calculus.covariant gains new functions: Cartan?, Christoffel?, Cartan->Christoffel, symmetrize-Christoffel, symmetrize-Cartan, Cartan->Cartan-over-map, geodesic-equation, parallel-transport-equation.

  • sicmutils.calculus.covariant/vector-field-Lie-derivative can now handle structural inputs.

New Functions, Functionality

• From #342:

  • Added sicmutils.calculus.derivative/D-as-matrix and sicmutils.matrix/as-matrix, ported from scmutils.

  • converted sicmutils.modint.ModInt to a deftype; this allows ModInt instances to be = to non-ModInt numbers on the right, if the right side is equal to the residue plus any integer multiple of the modulus. v/= gives us this behavior with numbers on the LEFT too, and ModInt on the right.

    • This change means that :i and :m won't return the residue and modulus anymore. sicmutils.modint gains new residue and modulus functions to access these attributes.

  • The JVM version of sicmutils gains more efficient gcd implementations for Integer and Long (in addition to the existing native BigInteger gcd), thanks to our existing Apache Commons-Math dependency.

  • sicmutils.structure/dual-zero aliases compatible-zero to match the scmutils interface. Both are now aliased into sicmutils.env.

  • Structure instances can now hold metadata (#339).

• From #339:

  • In sicmutils.mechanics.rotation:

    • gains aliases for R{xyz} in rotate-x, rotate-y and rotate-z.

    • R{x,y,z}-matrix now alias rotate-{x,y,z}-matrix.

    • Added new functions angle-axis->rotation-matrix and the mysterious, undocumented wcross->w from scmutils

    • rotate-{x,y,z}-tuple are now aliased into sicmutils.env.

  • Operator instances now ignore the right operator in operator-operator addition if the left operator passes a v/zero? test. Contexts are still appropriately merged.

  • in sicmutils.simplify.rules, the sqrt-contract ruleset now takes a simplifier argument and attempts to use it to simplify expressions internal to a square root. As an example, if two square roots in a product simplify to the same expression, we can drop the wrapping square root; otherwise multiplication is pushed under the root as before.

    • Added a missing rule in simplify-square-roots that handles roots of exponents with odd powers.

  • sicmutils.matrix changes:

    • generate has a new 2-arity version; if you supply a single dimension the returned matrix is square.

    • diagonal? returns true if its argument is a diagonal matrix, false otherwise.

  • A new namespace, sicmutils.util.permute:

    • factorial moved here from sicmutils.generic. It's still aliased into sicmutils.env.

    • new functions: permutations, combinations, cartesian-product, list-interchanges, permutation-parity, permutation-interchanges, permute, sort-and-permute, subpermute, number-of-permutations, number-of-combinations. See the tests for usage examples.

• From #338:

  • (* <structure> <operator>) multiplication pushes operator multiplication into the structure, rather than converting a structure into an operator.

• #337:

  • If you combine Operator instances with non-equal :subtype fields, the returned operator now keeps the parent subtype (or throws if one is not a subtype of the other).

  • Operator instances now ignore any identity?-passing operator on the left or right side of operator-operator multiplication. Contexts are still appropriately merged.

  • Similarly, Operator addition ignores zero? operators on the left or right side, and subtraction ignores zero? operators on the right right.

• #328:

  • Closes #249; operators now verify compatible contexts on multiplication.

  • Operator instances can now provides custom zero?, one?, identity?, zero-like, one-like and identity-like implementations by setting a function of a single (operator-typed) argument to a keyword like :zero? in their context. the identity operator returns true for identity?, and false for one? so that it isn't stripped by the g/* function.

  • structures implement the 0-arity case of IFn now.

• #335 implements g/make-rectangular, g/make-polar g/real-part and g/imag-part for clojure's Map data structure. Maps are treated as sparse vectors, any missing key on either side of make-rectangular or make-polaris treated as a 0 (rather than an error because the keys don't match, as in vectors).

• #334 adds implementations of g/add and the sicmutils.value.Value protocol for clojure's Set data structure. Addition is defined as set union, and (zero-like <set>) returns the empty set.

• #334 implements g/add, g/negate and g/sub for Clojure's Map data structure. Map addition is defined as a merge using g/add on clashing values; g/sub is the same, but any values on the right side not on the left side are negated.

  Maps can also be multiplied with scalars (commutatively) or divided (scalar on the right side only) by scalars. This, plus the commutative group property declared above, mean that Clojure's maps are sparse vector spaces over anything that responds true to sicmutils.value/scalar?... currently anything in the numeric tower up to complex, along with symbolic expressions and Differential instances.

0.17.0

(If you have any questions about how to use any of the following, please ask us at our Github Discussions page!)

This release starts the work of porting all of GJS and JW's "Functional Differential Geometry" to SICMUtils. The Differential Geometry section below describes the many new manifolds, coordinate systems and functions for interacting with these that we've gained.

The main big change in 0.17.0 that simplify no longer changes the type of its input; simplified expressions remain expressions.

solve-linear, solve-linear-left and solve-linear-right round out the stable of generics ported from scmutils.

They're not fully installed yet, but we've laid the groundwork for a new literal boolean type. This can represent equalities and inequalities, and will be excellent for equation solving.

Enjoy the release!

New Functions, Functionality

• #330 adds g/real-part and g/imag-part implementations for sicmutils.structure.Structure and sicmutils.matrix.Matrix instances. These pass through to the entries in the structure or matrix. #331 adds similar implementations for g/make-rectangular and g/make-polar.

• #327 adds sicmutils.structure/sumr, also aliased into sicmutils.env Given some function f and any number of isomorphic structures, sumr returns the sum of the results of applying f to each associated set of entries in each structure.

• #319 adds

  • symbolic boolean implementations for sym:=, sym:and, sym:or and sym:not with infix, latex and JavaScript renderers.
  • sym:derivative, for purely symbolic derivatives

  The boolean operators will act just like =, and and or on booleans, and appropriately respond if just one side is a boolean. If both sides are symbolic, These return a form like (= a b), (and a b) or (or a b).

  The functions currently live in sicmutils.numsymb only; access them via (numsymb/symbolic-operator <sym>), where <sym> is one of '=, 'and, 'or, 'not or 'derivative.

• #304 aliases sicmutils.operator/anticommutator, sicmutils.util/bigint? and into sicmutils.env

  • implements v/= properly for sequences, Differential, Complex, Structure and Matrix instances

  • in sicmutils.env, v/= now overrides clojure.core/=. v/= should act identically to clojure.core/= everywhere; the difference is that its behavior is customizable, so we can make Differential instances equal to numbers, or complex numbers with a 0 imaginary part equal to real numbers with the same real part.

    v/= may not drop recursively down into, say, Clojure maps. Please open an issue if you find a case like this!

  • BIG CHANGE: Literal and Structure instances now KEEP their type under g/simplify. If you want to get the expression back out of its Literal wrapper, use sicmutils.expression/expression-of, also aliased into sicmutils.env.

    This means that you can no longer make comparisons like this:

;; this worked before, and was used all over the tests (probably not in much
;; user code!)
(clojure.core/= '(* 3 x)
                (simplify (+ 'x 'x 'x)))
;;=> false

Instead, use v/= (which is now aliased into sicmutils.env):

;; `v/=` will do the right thing by unwrapping the literal expression on the
;; right:
(v/= '(+ x y) (+ 'x 'y))
;;=> true

• #305 adds g/solve-linear and g/solve-linear-left implementations between sicmutils.structure/Structure instances.

• #207:

  • adds missing implementations of g/floor, g/ceiling, g/integer-part and g/fractional-part for functions, both literal and abstract.

  • adds g/solve-linear, g/solve-linear-left, g/solve-linear-right. (g/solve-linear-right a b) returns x such that a = x*b, while g/solve-linear (and its alias, g/solve-linear-left) returns x such that a*x = b. These functions are implemented for:

    • sicmutils.series.{Series, PowerSeries}
    • all numeric types
    • functions, operators
    • sicmutils.modint.ModInt
    • sicmutils.differential.Differential, so you can differentiate through this operation

• #309: sicmutils.util/bigint is aliased as sicmutils.env/bigint in Clojurescript only. This is available natively in Clojure.

• #308 and #310 add:

  • sicmutils.ratio/{numerator,denominator,ratio?,rationalize} and are now aliased into sicmutils.env in Clojurescript. These are available natively in Clojure. sicmutils.complex/complex? is aliased into sicmutils.env for both platforms.

  • Proper superscript support in ->infix and ->TeX renderers.

• #306: Added the mathematical constants phi and e bound to, respectively, sicmutils.env/{phi,euler}.

Differential Geometry

• #326 is a large PR that marks the start of a big push toward full implementation of the ideas in "Functional Differential Geometry". Here is the full list of changes:

  • sicmutils.calculus.basis gains a new ::coordinate-basis type, along with coordinate-basis?, basis->coordinate-system, basis->dimension, contract and make-constant-vector-field from scmutils. More functions moved here.

  • In sicmutils.calculus.coordinate, let-coordinates and using-coordinates can now handle namespaced coordinate systems like m/R2-rect in their coordinate system position! Their docstrings are far better too.

  • sicmutils.calculus.vector-field/coordinate-basis-vector-fields was renamed to coordinate-system->vector-basis.

  • sicmutils.calculus.form-field/coordinate-basis-oneform-fields was renamed to coordinate-system->oneform-basis.

  • sicmutils.calculus.manifold gets a LOT of restructuring, and many new manifolds out of the box. Here's the full list of new functions:

    • manifold-type, patch-names, coordinate-system-names, manifold-point?, typical-coords, typical-point, transfer-point, corresponding-velocities
    • zero-manifold-function, one-manifold-function, constant-manifold-function

    And new manifolds and coordinate systems. Here's the full list of manifolds that are now present:

    • From the Rn family: R1, R2, R3, R4, spacetime
    • From S2-type: S2
    • From Sn: S1, S2p, S3
    • From SO3-type: SO3

    And coordinate systems, prefixed by their manifold in all cases:

    • R1-rect, the-real-line (alias for R1-rect)
    • R2-rect, R2-polar,
    • R3-rect, R3-cyl, R3-spherical,
    • R4-rect, R4-cyl,
    • spacetime-rect, spacetime-sphere

Behavior changes, bug fixes

• #329 fixes a bug where the simplifier couldn't handle expressions like (sqrt (literal-number 2)), where literal numbers with no symbols were nested inside of symbolic expressions.

• #321 changes the default TeX rendering style for down tuples back to horizontal, undoing #283. @kloimhardt made a solid case that because down tuples represent row vectors, it's not helpful for building knowledge and intuition to only distinguish these with differently-shaped braces. Intuition-builders win!

• #320: Operator gains a new simplifier for its name field; the simplifier applies the associative rule to products and sums of operators, collapses (adjacent) products down into exponents, and removes instances of identity (the multiplicative identity for operators).

  Operator multiplication (function composition) is associative but NOT commutative, so the default simplifier is not appropriate.

  Before this change:

sicmutils.env> (series/exp-series D)
#object[sicmutils.series.Series
  "(+ identity
      (* D identity)
      (* (/ 1 2) (* D (* D identity)))
      (* (/ 1 6) (* D (* D (* D identity)))) ...)"]

After:

sicmutils.env> (series/exp-series D)
#object[sicmutils.series.Series
  "(+ identity
      D
      (* (/ 1 2) (expt D 2))
      (* (/ 1 6) (expt D 3)) ...)"]

• #315: g/log2 and g/log10 on symbolic expressions now stay exact, instead of evaluating (log 2) or (log 10) and getting a non-simplifiable real number in the denominator:

(g/log2 'x)
;;=> (/ (log x) (log 2))

(g/log10 'x)
;;=> (/ (log x) (log 10))

• #304:

  • implements v/= properly for sequences, Differential, Complex, Structure and Matrix instances

  • in sicmutils.env, v/= now overrides clojure.core/=. v/= should act identically to clojure.core/= everywhere; the difference is that its behavior is customizable, so we can make Differential instances equal to numbers, or complex numbers with a 0 imaginary part equal to real numbers with the same real part.

    v/= may not drop recursively down into, say, Clojure maps. Please open an issue if you find a case like this!

  • BIG CHANGE: Literal and Structure instances now KEEP their type under g/simplify. If you want to get the expression back out of its Literal wrapper, use sicmutils.expression/expression-of, also aliased into sicmutils.env.

    This means that you can no longer make comparisons like this:

;; this worked before, and was used all over the tests (probably not in much
;; user code!)
(clojure.core/= '(* 3 x)
                (simplify (+ 'x 'x 'x)))
;;=> false

Instead, use v/= (which is now aliased into sicmutils.env):

;; `v/=` will do the right thing by unwrapping the literal expression on the
;; right:
(v/= '(+ x y) (+ 'x 'y))
;;=> true

• #207 fixes a bug where sicmutils.function/compose would fail when provided with no arguments. Now it appropriately returns identity.

• #310: g/make-rectangular and g/make-polar now return non-Complex numbers on the JVM if you pass 0 for the (respectively) imaginary or angle components. Previously this behavior only occurred on an integer 0; now it happens with 0.0 too, matching CLJS.

• #308 and #310: ->infix now renders any symbol named as an upper and lowercase greek characters ('alpha, 'Phi etc) as their proper unicode characters. 'ldots renders to '...', and 'ell renders to a pretty "ℓ", matching the TeX renderer.

0.16.0

(If you have any questions about how to use any of the following, please ask us at our Github Discussions page!)

This release contains a few correctness fixes, a number of new sicmutils.generic function implementations contributed by @pangloss, and a large expansion of the namespaces available to SCI-hosted environments.

The themes of the release are:

• Many new functions and functionality for existing types
• Upgraded rendering for forms like nested partials
• Better and better documentation!
• Easier interop with interactive hosts via SCI

A major goal was to develop SICMUtils into an environment that could host all of the exercises from the SICM textbook. We have many of those hosted at the https://github.com/sicmutils/sicm-exercises repository, and they all work and generate correctly rendered TeX!

The goals for the next release roll over from 0.15.0:

we'll focus on getting SICMUtils integrated with 2D and 3D rendering libraries like three.js, babylon.js and Quil. The long-term goal is for SICMUtils to support the sort of workflow I described in "The Dynamic Notebook".

Out-of-the-box charting and animation primitives are missing and sorely needed. Onward!

Detailed release notes:

New Functions, Functionality

• #278 adds new generic floor, ceiling, integer-part and fractional-part generic functions, along with:

  • implementations for all types in the numeric tower - ratios, integers, reals, complex, and Differential (so derivatives of these functions work!)
  • symbolic expression implementations
  • symbolic implementations for modulo and remainder
  • new support for these four generics plus modulo and remainder in function compilation via sicmutils.expression.compile (#295)
  • rendering support by ->infix, ->TeX, ->Javascript (#295)

  Thank you to @pangloss for this major contribution!

• division between two Structure instances a and b now (as of #297) returns a new structure instance (/ a b) that matches the contract (= a (* b (/ a b))). Previously, the division would not necessarily contract with b to return a, resulting in problems with the double pendulum exercise of #296.

• #149 adds a sicmutils.modint/modint? predicate, and sicmutils.modint/chinese-remainder. The latter efficiently performs the Chinese Remainder algorithm for solving systems of linear congruences. Available via sicmutils.env/chinese-remainder.

• clojure.lang.Var implements the sicmutils.value/Value protocol, allowing it to respond appropriately with its name to v/freeze (#298).

• Install sicmutils.generic/{quotient,modulo,remainder,partial-derivative} into sicmutils.env (#273). Thanks to @pangloss for pointing out that these were missing!

• #284 added:

  • new functions sicmutils.mechanics.lagrange/acceleration-tuple for creating the acceleration entry in a local tuple

  • sicmutils.mechanics.lagrange/acceleration for extracting the acceleration component of a local tuple

  • An upgraded sicmutils.mechanics.lagrange/F->C to handle local tuples of arbitrary length. This version of F->C is more general than the version from the textbook that was previously included.

  These are all aliased in sicmutils.env, along with a new Γ-bar alias for sicmutils.mechanics.lagrange/Γ-bar.

• #282 modifies the sicmutils.value/freeze implementation for Clojure vector to freeze vectors into the same representation as an up structure. This makes rendering these forms much more simple and matches the scmutils behavior.

• sicmutils.structure.Structure implements clojure.lang.{Indexed, IReduce} on the JVM, allowing it to act more like a vector (#282). (The CLJS implementation already did this.) (vec (up 1 2 3)) now works correctly.

• Series, PowerSeries and Operator can hold metadata and respond properly to meta and with-meta (#265). sicmutils.series/{->Series, ->PowerSeries} and sicmutils.operator/->Operator all take a new arity for metadata.

g/simplify changes

• g/simplify called with an argument x of type Series, PowerSeries, Matrix, Operator, Complex and sicmutils.abstract.function/Function now return an instance of type x, performing appropriate simplifications if possible. before #297 and #298, these operation would return bare symbols or sequences.

  A future release will make this change for Structure and Literal too, once #255 is resolved.

Rendering, Docs

• #286 adds a batch of rules to sicmutils.simplify.rules/canonicalize-partials that act to gather up nested partial (derivative) applications into products and exponentiated partials. ->TeX and ->infix both produce better-looking forms with this change.

  This example shows how g/simplify can organize a nested application of many partial derivatives into a product:

(let [f (literal-function 'f (-> (UP Real Real) Real))]
  (simplify
   (((partial 0)
     ((partial 1)
      ((partial 0) f))) (up 'x 'y))))
;;=> (((* (expt (partial 0) 2) (partial 1)) f) (up x y))

• #283 changes the default TeX rendering style for down tuples to vertical vs horizontal.

• Symbols like 'qprime ending with prime or primeprime will render as q' or q'' respectively in TeX, rather than the fully-spelled-out \mathsf{qprime} (#282).

• #280 adds a new :equation keyword argument to sicmutils.render/->TeX. If you pass a truthy value to :equation, the result will be wrapped in an equation environment. :equation <string> will insert a \\label{<string>} entry inside the equation environment.

  • sicmutils.env/->tex-equation is identical to #(sicmutils.render/->TeX (g/simplify %) :equation true); If you pass a :label keyword argument to ->tex-equation it will be forwarded to ->TeX, creating the expected label entry.

• #279: Function aliases in sicmutils.env now properly mirror over docstrings and other Var metadata, thanks to Potemkin's import-def. This doesn't quite work in Clojurescript since we can't use resolve inside of a macro (special form!).

• Add a proper namespace to demo.clj, to make it easier to use outside of lein repl (#264).

SCI Upgrades

• #289 adds many namespaces to sicmutils.env.sci:

  • sicmutils.{complex,expression,modint,numsymb,polynomial,ratio,rational-function,util,value}

  • sicmutils.abstract.number

  • sicmutils.expression.analyze

  • sicmutils.numerical.elliptic

  • sicmutils.util.{aggregate,stream}

  • #289 also introduces sicmutils.function/*strict-arity-checks* to allow the user to toggle whether or not to throw exceptions if the system thinks that arities are incompatible. It turns out that inside of an SCI environment, the usual tricks for detecting arities fail, causing errors in many expressions. To get around this, *strict-arity-checks* is FALSE by default.

Behavior changes, bug fixes

• In JVM Clojure (as of #298), sicmutils.expression.compile defaults to clojure.core/eval to compile functions, while Clojurescript defaults to SCI. The performance is much faster for numerical routines and worth the slightly different default behavior.

  To use to SCI compilation on the JVM, wrap your form in a binding:

  (require '[sicmutils.expression.compile :as compile])
  
  (binding [compile/*mode* :sci]
    (my-compiler-triggering-function))

  To set the mode permanently, use compile/set-compiler-mode!:

  (compile/set-compiler-mode! :sci)
  
  (my-compiler-triggering-function)

  The options allowed as of 0.16.0 are :sci and :native.

• #292 fixes a StackOverflow that would sometimes appear when comparing symbolic expressions to non-expressions. (= (literal-number x) y) now returns true if (= x y) (AND, in clj, if y is not a collection!), false otherwise. #255 is currently blocking pass-through equality with collections on the JVM. Thanks to @daslu for the report here!

• sicmutils.modint/make now verifies with a precondition that its two arguments are both v/integral? (#298). We need this constraint now that g/modulo is defined for more types.

• #285 fixes a bug that prevented sin / cos from simplifying into a tan in the numerator, and makes seq:- slightly more efficient (closing heisenbug #151).

0.15.0

(If you have any questions about how to use any of the following, please ask us at our Github Discussions page!)

This release was focused on a small number of themes:

Automatic differentiation:

The goal for this cycle's automatic differentiation (AD) work was to expand the set of functions and types that can play with AD. AD now works on functions that return all Clojure sequences, maps, and vectors, in addition to SICMUtils types like Operator, Series, PowerSeries and Structure. The system is now fully extensible, so if you want to differentiate functions that return custom records or Java collections, it's now no problem.

SICMUtils can now differentiate functions in Clojurescript that use comparison operations like <, =, <= and friends. Clojure can't quite do this yet, but you can differentiate through v/compare and v/= calls.

We can also differentiate functions that return other functions with no trouble; only a few libraries can do this, and the behavior is subtle. Hold tight for comprehensive docs describing this behavior.

New Div, Grad, Curl and Lap operators build on this foundation.

SCI Integration

To support safe execution inside of a browser-based Notebook or REPL environment, SICMUtils now has full support for @borkdude's SCI, the Small Clojure Interpreter, via the sicmutils.sci namespace. Every function and macro in the library now works in SCI. (Thanks for @borkdude and @mk for your help and contributions.

Rendering

@hcarvalhoalves made a number of contributions to the LaTeX and infix renderers; PowerSeries and Series now render beautifully, as well as = and the various inequality symbols. Expect a lot more action here as we move into more browser-based notebook environments.

There's a lot more that went into this release; give the detailed notes below a look for more details.

What's coming next?

The next release will focus on getting SICMUtils integrated with 2D and 3D rendering libraries like three.js, babylon.js and Quil. The long-term goal is for SICMUtils to support the sort of workflow I described in "The Dynamic Notebook". This will require a big push on generic, pluggable representations for the various types and expressions in the library.

Thanks again to @hcarvalhoalves and @mk for their contributions, and to @borkdude for his help with SCI!

On to the detailed release notes:

Automatic Differentiation

• New, literate Differential implementation lives at at sicmutils.differential (#221) (see this page for a readable version.) Notable changes to the original impl at sicmutils.calculus.derivative include:

  • We've changed our terminology from GJS's finite-part, infinitesimal-part, make-x+dx to the more modern primal-part, tangent-part, bundle-element that the Automatic Differentiation community has adopted. His comment is that he doesn't take terms from mathematics unless he's sure that he's using it in the correct way; the safer way is to stick with his terms, but we go boldly forth with the masses.

  • A new sicmutils.differential.IPerturbed protocol makes it possible to extend the Automatic Differentiation (AD) system to be able to handle different Functor-shaped return values, like Java or JS lists and objects. See the cljdoc page on Automatic Differentiation for more detail.

    • #222 implements d/IPerturbed for Clojure maps, vectors and sequences; all are now valid return types for functions you pass to D.

    • #222 also implements d/IPerturbed for SICMUtils Matrix, Structure, Series, PowerSeries and Operator.

    • #223 implements d/IPerturbed for Clojure functions and multimethods, handling the attendant subtlety that fixes "Alexey's Amazing Bug".

  • sicmutils.differential/{lift-1,lift-2,lift-n} allow you to make custom operations differentiable, provided you can supply a derivative.

  • Differential implements sicmutils.function/arity, IFn, and can be applied to arguments if its coefficients are function values. Differential instances also v/freeze and g/simplify properly (by pushing these actions into their coefficients).

  • New compare and equiv implementations allow Differential instances to compare themselves with other objects using only their primal parts; this makes it possible to use functions like <=, >, = to do control flow during automatic differentiation. (Use compare-full and eq if you want to do full equality comparisons on primal and tangent components.)

  • related, g/abs is now implemented for Differential instances, making this function available in functions passed to D.

  • proper numerical?, one? and identity? implementations. The latter two only respond true if there are NO tangent components; This means that one? and (= % 1) will not agree.

  • The new implementation fixes a subtle bug with nested, higher order automatic differentiation - it's too subtle for the CHANGELOG, so please the "amazing" bug sections in sicmutils.calculus.derivative-test for proper exposition.

• #223 converts the implementation of sicmutils.calculus.derivative/D to use the new Differential type; this fixes "Alexey's Amazing Bug" and allows D to operate on higher order functions. For some function f that returns another function, ((D f) x) will return a function that keeps x "alive" for the purposes of differentiation inside its body. See sicmutils.calculus.derivative-test/amazing-bug for an extended example.

• sicmutils.generic/partial-derivative gains a Keyword extension, so it can respond properly to :name and :arity calls (#221).

• D (or sicmutils.generic/partial-derivative) applied to a matrix of functions now takes the elementwise partials of every function in the matrix. (#218)

• #253 moves the derivative implementations (where relevant) onto the metadata of generic functions. You can access these by calling (<generic-function> :dfdx) or (<generic-function> :dfdy), depending on whether the generic is unary or binary. #253 also changes the name of macro sicmutils.generic/def-generic-function to sicmutils.generic/defgeneric.

Rendering

• sicmutils.expression/Literal instances now use pr-str to generate a string representation; this allows this type to wrap lazy-sequence expressions such as those returned from g/simplify (#259)

• sicmutils.expression.render/->infix and sicmutils.expression.render/->TeX now handle equality/inequality symbols (=, >=, >, ...) as infix (#257).

• sicmutils.expression.render/*TeX-sans-serif-symbols* binding to control if symbols longer than 1 char should have \mathsf applied (#258).

• ->infix, ->TeX and ->JavaScript in sicmutils.expression.render can now accept unfrozen and unsimplified Expression instances (#241). This makes it a bit more convenient to use ->infix and ->TeX at the REPL, or in a Notebook environment. Additionally, the return values of renderers are always coerced to strings. (Previously, (->infix 10) would return a number directly.)

• up and down tuples from sicmutils.structure gain a proper print-method implementation (#229); these now render as (up 1 2 3) and (down 1 2 3), instead of the former more verbose representation (when using pr.)

• sicmutils.render/->infix and sicmutils.render/->TeX will render Series and PowerSeries as an infinite sum (showing the first four terms). In the case of unnaplied PowerSeries, it will represent the unbound variable as _ (#260).

Performance Improvements

• sicmutils.modint gains more efficient implementations for inverse, quotient, exact-divide and expt on the JVM (#251).

Comparison / Native Type Integration

• beefed up the Javascript numeric tower to allow objects like sicmutils.differential/Differential, sicmutils.expression/Expression and friends that WRAP numbers to compare properly using cljs-native <, <=, =, >= and > (#236)

• new sicmutils.value/compare function exposed in sicmutils.env returns a valid comparison bit between native numbers and numbers wrapped in Differential or Expression in both JVM Clojure and Clojurescript (#236). The behavior matches clojure.core/compare for all reals on the JVM; it doesn't in Clojurescript because native compare can't handle goog.math.{Long,Integer} or js/BigInt.

Operator

• #219 introduces a number of changes to Operator's behavior:

  • Operator is now a deftype (not a defrecord); the keyword lookup for its :name, :arity, :context and :o fields have been replaced by, respectively, o/name, sicmutils.function/arity, o/context and o/procedure functions. This change happened to allow Operator to implement protocols like ILookup.

  • Native get and get-in now act on Operator. Given an operator function f, get and get-in compose #(get % k), or similar with f. This deferred action matches the effect of all sicmutils generics on functions.

  • Combining an operator and a non-operator via + and -, the non-operator was previously lifted into an operator that multiplied itself by the new operator's argument. As of #219, this "multiplication" uses the operator definition of multiplication - meaning, the new operator composes the non-operator with its argument. Where does this matter?

    Previously adding the non-operator sicmutils.function/I to the identity operator I would act like this:

    (((g/+ o/identity f/I) f/I) 10)
    ;; => 110 == (+ 10 (* 10 10))

    Because f/I multiplied itself by its argument... resulting in (* f/I f/I) == g/square.

    After the change, you see this:

    (((g/+ o/identity f/I) f/I) 10)
    ;; => 20

    because f/I composes with its argument.

  • sicmutils.operator/identity-operator has been renamed to sicmutils.operator/identity

  • o/make-operator now takes an explicit context map, instead of a multi-arity implementation with key-value pairs.

  • Operator now implements g/negate.

  • g/cross-product is no longer implemented for Operator. operators were introduced by GJS to act like "differential operators", can only add, negate and multiply (defined as composition). We will probably relax this in the future, and add more functions like g/cross-product that compose with the operator's output; but for now we're cleaning house, since this function isn't used anywhere.

  • In this same spirit, Operator instances can now only be divided by scalars (not functions anymore), reflecting the ring structure of a differential operator.

Additions

• #224 adds new Div, Grad, Curl and Lap operators in sicmutils.calculus.derivative and installs them into sicmutils.env. #224 also removes the g/transpose implementation for Operator instances, and exposes sicmutils.calculus.derivative/taylor-series to sicmutils.env.

• #222 adds v/Value implementations for Clojure sequences and maps. Maps and vectors implement f/Arity and return [:between 1 2]. zero?andzero-likework on sequence entries and map values. Maps can specify theirv/kindreturn value with a:typekey, and some of the calculus implementations do already make use of this feature.g/partial-derivative` on a Clojure Map passes through to its values.

• As of #232, sicmutils.expression.compile/compile-univariate-fn is now compile-fn (same change for the non-cached compile-fn* in the same namespace). The new implementation can compile arguments of any arity, not just arity == 1. The new version takes an arity parameter n that defaults to (sicmutils.function/arity f).

• sicmutils.function/arity is now a protocol method, under the sicmutils.function/IArity protocol (#218). In addition to functions, arity now correctly responds to:

  • sicmutils.matrix/Matrix: calling arity on a matrix assumes that the matrix has function elements; the returned arity is the most general arity that all functions will respond to.
  • sicmutils.operator/Operator: returns the arity of the operator's wrapped function.
  • sicmutils.series/Series: arity on a Series assumes that the series contains functions as entries, and returns, conservatively, the arity of the first element of the series.
  • sicmutils.series/PowerSeries: arity returns [:exactly 1], since PowerSeries are currently single variable.
  • vectors, and sicmutils.structure/Structure: arity on these collections assumes that the collection contains functions as entries, and returns the most general arity that is compatible with all of the function elements.

• New single-arity case for sicmutils.structure/opposite returns an identical structure with flipped orientation (#220). acts as identity for non-structures.

• Added missing identity?, identity-like for complex and rational numbers (#236)

• sicmutils.env/ref now accepts function and operators (#219). (ref f 0 1), as an example, returns a new function g that acts like f but calls (ref result 0 1) on the result.

• The slightly more general sicmutils.env/component replaces sicmutils.structure/component in the sicmutils.env namespace (#219). ((component 0 1) x) == (ref x 0 1).

• New functions sicmutils.function/{get,get-in} added that act like the clojure.core versions; but given a function f, they compose #(get % k), or similar with f. This deferred action matches the effect of all sicmutils generics on functions. (#218)

• sicmutils.function/I aliases clojure.core/identity (#218). #219 exposes I in sicmutils.env.

• sicmutils.env.sci contains an SCI context and namespace mapping sufficient to evaluate all of sicmutils, macros and all, inside of an SCI environment (#216). Huge thanks to @borkdude for support and @mk for implementing this!

• sicmutils.numerical.elliptic gains a full complement of elliptic integral utilities (#211):

  • Carlson symmetric forms of the elliptic integrals: carlson-rd, carlson-rc, carlson-rj (carlson-rf was already present)
  • Legendre elliptic integrals of the second and third forms, as the two-arity forms of elliptic-e and elliptic-pi (elliptic-f already existed)
  • the complete elliptic integrals via elliptic-k (first kind) and the single-arity forms of elliptic-e and elliptic-pi
  • k-and-deriv returns a pair of the complete elliptical integral of the first form, elliptic-k, and its derivative with respect to k.
  • jacobi-elliptic-functions ported from scmutils and Press's Numerical Recipes

Fixes / Misc

• The operator returned by sicmutils.calculus.derivative/partial now has a proper name field like (partial 0), instead of :partial-derivative (#223).

• #223 fixes a problem where (operator * structure) would return a structure of operators instead of an operator that closed over the multiplication. ::s/structure is now properly a ::o/co-operator, matching its status as a ::f/cofunction.

• Fix a bug where f/arity would throw an exception with multiple-arity functions on the JVM (#240). It now responds properly with [:between min-arity max-arity], or [:at-least n] if there is a variadic case too.

• #238 converts sicmutils.abstract.function/Function from a defrecord to a deftype, fixing a subtle bug where (empty f) was getting called in a nested derivative test.

• fixed bug with g/dimension for row and column matrices (#214). previously they returned 1 in both cases; now they return the total number of entries.

• #253 adds proper :arglists metadata for all generic functions.

0.14.0

• After the work below, v/nullity? renamed to v/zero?, and v/unity? renamed to v/one? (#180). This affects the names listed in the CHANGELOG entries below.

Miscellaneous

• expose bootstrap-repl! to Clojurescript, so that this is available in self-hosted CLJS (#157)

• modified infix.cljc to wrap forms in displaystyle and add proper carriage returns inside structures (#157)

• add multidimensional-minimize to the sicmutils.env namespace (#157)

• add more sqrt simplification rules to allow square roots to cancel out across a division boundary, with or without products in the numerator and denominator (#160)

• fix NPE bug that appears in nelder-mead, when callback isn't supplied (#162)

• Add sqrt-expand and sqrt-contract, to allow simplifications to push inside of square roots (#163)

• speed up power series multiplication by skipping work when either head term is zero (#166)

• File moves:

  • sicmutils.polynomial-gcd => sicmutils.polynomial.gcd
  • sicmutils.polynomial-factor => sicmutils.polynomial.factor
  • sicmutils.rules => sicmutils.simplify.rules
  • sicmutils.analyze => sicmutils.expression.analyze
  • sicmutils.infix => sicmutils.expression.render
  • sicmutils.numerical.compile => sicmutils.expression.compile

• sicmutils.env/one? now exposes/aliases sicmutils.value/unity? #154

• Fixed #93 by adding an explicit g/invert implementation for polynomials in the rational fn namespace. The fix lives in #169.

• added sicmutils.value/sqrt-machine-epsilon (#170)

• fixed issues in function.cljc and operator.cljc where the Clojurescript IFn -invoke arguments shadowed either the this operator, or some parameter name in the deftype (#169)

• g/sqrt now maintains precision with Clojurescript's rational numbers. (g/sqrt #sicm/ratio 9/4) for example returns #sicm/ratio 3/2. (#168)

• g/determinant and g/transpose now act as identity for everything in the numeric tower, plus symbolic expressions (#168)

• sicmutils.expression.Expression is now sicmutils.expression.Literal; it has a new meta field, and is a deftype instead of a defrecord. (#168)

  • To get the internal expression, use x/expression-of instead of :expression.
  • to access the type field, use x/literal-type instead of :type

• 2-arity g/atan, g/cross-product and g/gcd now work for functions (#168)

• Literal now responds appropriately to v/unity? and v/nullity? if it wraps a numerical "0" or "1". v/exact? now returns true if the literal wraps an exact number (#168)

• x/variables-in now works with wrapped expressions; no more need to explicitly unwrap (#168)

• x/walk-expression renamed x/evaluate (#168)

• The new x/substitute performs substitutions on an unwrapped expression (#168)

• x/compare returns a comparator that works with unwrapped symbolic expression trees (#168). The rules are that that types have the following ordering:

• empty sequence is < anything (except another empty seq)

• real < symbol < string < sequence

• sequences compare element-by-element

• Any types NOT in this list compare using hashes

• g/transpose now works properly for functions that act as linear maps. The defining relation is:

(= (((transpose f) g) 'x)
   (g (f x)))

• added g/determinant implementation to functions (#171)

• Moved all literal-function machinery and definitions to sicmutils.abstract.function (#171). sicmutils.function now contains only the generic method implementations for clojure functions and multimethods.

• Switched inheritance order for functions; :sicmutils.abstract.function/function (used to be :sicmutils.function/function) now inherits from ::v/function instead of the other way around. (#171)

• Enhanced the g/simplify behavior for core functions that overlap with generic functions (+, -, *, /, mod, quot, rem, neg?). These now freeze to the same symbols as their generic counterparts. (#173)

• Add support for the hyperbolic trig functions sinh, cosh, tanh, atanh, asinh and acosh to sicmutils.expression.render/->Javascript. (#174)

• Add support for the hyperbolic trig functions atanh, asinh and acosh to sicmutils.expression.compile. (#175)

• matrix.cljc gains m/nth-col and m/diagonal (#178 introduces:)

• As of #178 introduces:, we have three new kinds for matrices. Square matrices return ::m/square-matrix, and columns and rows return ::m/column-matrix and ::row-matrix respectively. These all derive from ::m/matrix. This makes it easier to register methods or test specifically for these cases. We've also added m/column? and m/row? predicates to check for these cases.

• #185 specializes all matrix operations that return power series (trig operations and g/exp to ::square-matrix).

• #184 modifies v/exact? on functions; ((v/exact? f) x) == (v/exact? (f x)) now, instead of false as before. literal-function forms now have a correct v/one-like implementation.

• clojure Vars now respond to function algebra (#184). All functions implement g/negative?, g/abs, g/quotient, g/remainder, g/modulo, g/dimension and g/exact-divide, responding to the appropriate arities.

• sicmutils.complex/complex can now take any real type in its constructor, vs only numbers (#184).

• modint instances now implement v/freeze?: (sicmutils.modint/make 1 2) freezes to that (modint 1 2). (#185).

• v/eq renamed to v/=. (#186).

• v/zero-like on matrices now fills entries with appropriate v/zero-like versions of their existing types (#188)

• v/Value gains identity-like and identity (#188). These are aliased into sicmutils.env. Implementations are installed on:

  • all numeric types, symbolic expressions, Differential (they return 1 of the appropriate type)
  • native and abstract functions, vars (they return an identity function)
  • operators (return an identity operator, same as one-like)
  • matrices (identity matrix, only works with ::m/square-matrix)
  • Polynomial (only works on monomials for now, returns an identity polynomial)
  • RationalFunction (returns the identity poly divided by unit poly, so only works on monomials by extension)
  • ModInt (returns the same as one-like)
  • Series and PowerSeries (returns [0 1 0 0 0 0...]). This is slightly suspect in the case of Series, since Series, unlike PowerSeries, are general infinite sequences and not necessarily interpreted as polynomials. This decision follows scmutils convention.

• sicmutils.complex/I aliases i (#189)

• matrix.cljc has a new by-cols (analogous to m/by-rows), and row to generate a row matrix (analagous to column). #197 Also in matrix.cljc:

  • num-rows, num-cols access the row or column number without inspecting the deftype variables directly
  • fmap-indexed, like fmap but receives i and j indices as second and third arguments.
  • with-substituted-row, for swapping out a single row in a matrix
  • submatrix generates a submatrix from low and high row and cols
  • matrix-some renamed to some: make sure to use a namespace prefix to avoid clashing with clojure.core/some.
  • new-matrix constructor by-cols (analogous to by-rows, takes a sequence of columns)
  • row constructor takes a sequence of values and returns a row matrix.
  • by-rows*, by-cols*, row* and column* are non-variadic versions of those functions. If you already have a sequence of rows, columns or elements, prefer these.
  • up->row-matrix => down->row-matrix and row-matrix->up => row-matrix->down. A row is analogous to a down, so we make a change to reflect this.
  • g/cross-product between two down structures now returns a down.
  • make-zero generates a zero-valued matrix of the supplied dimensions.
  • make-diagonal generates a diagonal matrix containing the values of the supplied sequence.
  • m/identity-like returns an identity matrix (given a square matrix) with entries of identical type, but set appropriately to zero or one. This is installed as v/one-like and v/identity-like.
  • v/identity? now returns true for identity matrices, false otherwise. v/one? returns false for identity matrices! If it didn't, (* 2 (I 10)) would return 2, since one? signals multiplicative identity.

• sicmutils.structure/up and sicmutils.structure/down now have analogous s/up* and s/down* functions. These behave identically, but are non-variadic. If you already have a sequence you'd like to transform, prefer these (#197).

• sicmutils.value/kind-predicate takes some item and returns a predicate that returns true if its argument has the same type (or inherits from it) (#197).

• sicmutils.function/arg-shift and sicmutils.function/arg-scale take functions and return new functions that shift and scale their arguments (respectively) by the originally supplied shifts (#197).

• sicmutils.generic/factorial computes the factorial of the supplied integer n. (#197).

• Many new functions and constants exposed in sicmutils.env via #197:

  • -pi joins pi as a constant
  • s:generate, m:generate, vector:generate to generate matrices, structures and vectors
  • constant-series, from series/constant
  • seq:print and seq:pprint
  • matrix-by-cols, row-matrix, v:make-basis-unit
  • aliases for sicmutils.function's arity, arg-shift, arg-scale
  • dimension, factorial aliased from sicmutils.generic
  • derivative aliased from sicmutils.calculus.derivative
  • submatrix, up->column-matrix, down->row-matrix, row-matrix->{down,vector}, column-matrix->{up,vector} aliased from sicmutils.matrix
  • D-numeric from sicmutils.numerical.derivative
  • brent-min, brent-max, golden-section-min, golden-section-max
  • nelder-mead
  • sum from `sicmutils.util.aggregate
  • kind-predicate from sicmutils.value

• Structures and matrices both gain the ability to do native get-in, assoc-in and empty. These work as expected, like a potentially nested vector. (#193)

• matrix.cljc gains up->row-matrix, up->column-matrix, row-matrix->up, column-matrix->up (#193)

• structure.cljc gains many features in (#193):

  • kronecker and basis-unit for generating potentially infinite basis sequences
  • the ability to conj new items onto a structure: (conj (up 1 2) 3) => (up 1 2 3)
  • The structure-preserving map-chain takes a 2-arg function and presents it with each element of a deeply nested structure, along with a vector of its "chain", the path into its location. The fn's return becomes the new item at that location.
  • structure->prototype generates a same-shape structure as its argument, with symbolic entries that display their location (preserving orientation).
  • typical-object returns a structure of the same shape and orientation as s, generated by substituting gensymmed symbols in for each entry.
  • compatible-zero returns a structure compatible for multiplication with s down to 0.
  • transpose-outer returns a new structure with the same orientation as the first element of s, filled with elements of the same orientation as s. Each element is generating by taking the first element of each entry in s, the the second, etc... In that sense this is similar to a traditional matrix transpose.
  • dot-product takes the dot product of two structures. They must be the same top-level orientation and dimension; beyond that, their entries are pairwise-multiplied and summed.
  • inner-product is the same, but the left structure is conjugated first.
  • outer-product now works multiple levels deep.
  • vector-outer-product and vector-inner-product are similar, but only enforce the top-level length; all internal structures are NOT flattened and must be compatible for g/*.
  • compatible-for-contraction? now searches recursively down into a structure; previously it only checked the top level.
  • The new *allow-incompatible-multiplication* dynamic variable is set to true by default. Set it false to force a setting where, when you multiply structures, they must be:
    • opposite orientation
    • every element of the right entry must be compatible for contraction with the left
  • structure multiplication with scalars, etc now respects ordering, just in case any multiplication is not commutative.
  • sicmutils.generators now holds generators for up, down, and structure generators; these produce potentially deeply nested structures. up1, down1 and structure1 generate only one level deep. Mix and match! See structure_test.cljc for many examples of how to use these.

Literals

• literal-matrix fn generates a symbolic matrix (#169)
• literal, literal-up and literal-down generate symbolic structures (#169)

Numeric Tower Adjustments

This release (courtesy of #168) brings the numeric tower in line with the scmutils tower. Prior to this release, all numbers, including complex, descended from ::x/numerical-expression. Symbolic expressions also derived from this type! The problem this causes is that all of generic implementations for the number types default to the symbolic functions.

If I don't specify a g/sec method for numbers, for example, then (g/sec 12) returns a symbolic (/ 1 (cos 12)), instead of actually evaluating the expression.

The fix comes from these changes:

• ::v/number now means, "the numeric tower ascending from integer -> rational -> real -> complex numbers. All of these types now respond true to v/number? (prior to this release, Complex numbers did NOT!)

• ::v/real now means, "anything in the numeric tower except Complex". These all respond true to v/real?

• ::x/numeric-expression has changed to ::x/numeric, and now means "anything that responds to ::"v/number, plus symbolic expressions, which now clearly represent any number in the numeric tower. Query for these with v/scalar?

I can now make some comments that clear up my former misunderstandings:

• The sicmutils.abstract.number (I'll call this an here) namespace is responsible for installing generic implementations of all numeric methods for symbolic expressions and "literal numbers".

• the an/literal-number constructor promotes a number, symbol or symbolic expression up to :xx/numeric, which means that any operation you perform on it will pass it through the symbolic expressions defined in sicmutils.numsymb. A few notes on these expressions:

  • They will try to preserve exactness, but if they can't - ie, if you do something like (cos (an/literal-number 2.2)) - the system will return -.588. If you call (cos (an/literal-number 2)), you'll get the expression (cos 2), preserving exactness.

  • Symbols are automatically interpreted as "literal numbers".

  • The only ways to make a proper symbolic expression that works with the generics are:

    • Use the explicit an/literal-number constructor
    • pass a symbol to any generic arithmetic function
    • perform any unary or binary arithmetic operation on an existing symbolic expression.

  • an/abstract-number? returns true for symbolic expressions, anything wrapped in literal-number or symbols.

  • literal-number? only returns true for explicitly wrapped things and symbolic expressions, not symbols.

  • use v/real?, v/number? and v/scalar? to query the numeric tower.

• If you want to compare literal numbers and an expression like (an/literal-number 12), use v/=. In Clojurescript, this will work with the built in = as well, since equality is implemented with a protocol that we can extend. For example:

(v/= 12 (literal-number 12))
;;=> true

(= 12 (literal-number 12))
;; true in cljs, false in clj

If you keep the literal on the left side of =, this will work in both systems, since we've overridden the = implementation for literals:

(= (literal-number 12) 12)
;;=> true in both languages

This paves the way for the other abstract types that exist in scmutils, like matrices, up and down tuples.

New Generic Functions

This release brings us closer to the interface provided by scmutils.

PR #193 brings:

• g/dot-product, for scalars, differentials, structures, functions and row/column matrices
• g/inner-product for scalars, structures, functions and row/column matrices
• g/outer-product for functions, structures of length 3 and matrices, between a row and a column only
• g/cross-product now works for row/column matrices in addition to structures (and functions that accept these)

PR #169 brings:

• g/exp2, g/exp10 for exponents with base 2 and 10
• g/log2, for base 2 logarithms
• g/log10 for base 10 logs
• g/gcd and g/lcm are now exposed in sicmutils.env

#178 introduces:

• g/dimension for scalars (always 1), structures and matrices (square, column and row)
• g/trace returns the trace for square matrices and square structures

We now expose the following additional trigonometric functions in sicmutils.generic (courtesy of #154):

• cosh: hyperbolic cosine
• sinh: hyperbolic sine
• tanh: hyperbolic tangent, ie sinh/cosh
• sech: hyperbolic secant, ie 1/cosh
• csch: hyperbolic secant, ie 1/sinh
• acosh: inverse hyperbolic cosine, ie, (= x (cosh (acosh x)))
• asinh: inverse hyperbolic sine, ie, (= x (sinh (asinh x)))
• atanh: inverse hyperbolic tangent, ie, (= x (tanh (atanh x)))

These three methods existed in sicmutils.env, but not as extensible generics. Now they're fully extensible:

• cot: cotangent, ie 1/tan
• sec: secant, ie 1/cos
• csc: cosecant, ie 1/sin

These all work with:

• real and complex numbers
• power series (missing a few implementations, operators and matrices are missing the same ones for this reason)
• matrices (square matrices return their power series expansions)
• operators (power series expansion of the operator)
• functions (where they create composition)
• symbolic expressions
• Derivatives and dual numbers! The new functions all work with D, the forward-mode automatic differentiation operator.

Additionally, four methods that lived in sicmutils.generic are now exposed as generics:

• real-part
• imag-part
• angle
• conjugate

These now work on:

• all numeric types, including symbolic expressions.

• functions

• structures (only magnitude and conjugate)

  • magnitude formerly didn't handle structures containing complex numbers by taking a proper inner product. This is fixed as of #168

• PR #189 introduces:

  • g/make-rectangular, (build a complex number from real and imaginary parts)
  • g/make-polar (build a complex number from radius and angle)
  • note that these work with real numbers, symbolic numbers, functions and any combination of these.

These work with functions, real numbers and symbolic expressions (and any mix of the three).

0.13.0

The main announcement for this release is Clojurescript Support!. Implementing this resulted in a few upgrades along the way:

• more powerful numerics, specifically definite-integral and native minimization routines
• a generic numeric tower for Clojurescript
• Many more tests! The test coverage was great before, and it's stayed high as we've added new implementations.
• added explicit code coverage metrics via Codecov:

Here are more explicit details on the release.

Misc

generic.cljc now includes a default implementation of:

• expt given a valid mul
• default sub, given a valid add and negate
• default div, given a valid mul and invert
• Expression and Operator both have better print-method implementations, so the repl experience feels more like scmutils
• Operator now has an expn method, which acts like g/exp on an operator but expands each term in order n.
• many, many more tests!

Clojurescript Support

Full conversion of SICMUtils to Clojurescript. All functionality from v0.12.1 now works in both Clojure and Clojurescript!

Most of the conversion was straightforward. The major missing piece was a numeric tower implementation for Clojurescript (complex numbers, ratios) that bring it up to parity with Clojure:

• Add the bigfraction implementation from fraction.js sicmutils.ratio for cross-platform ratio support (#99)
• Adds CLJS complex number support through complex.js (#41)
• js/BigInt, goog.math.Long and goog.math.Integer implementations round out the numeric tower (#45)

Numerical Routines

The numerical routines in SICMUtils depend heavily on Apache Commons, which of course only exists in Java. We had to implement much of the numerics code in native Clojure. It's fast, efficient and functional. Give it a read if you're curious about how these algorithms work.

• New, native minimization routines have replaced the Apache Commons implementations:

  • Univariate Minimizers

    • Port scipy's auto-bracketing + scmutils version (#104)
    • Port golden section search from scipy (#105)
    • Implement Brent's method for fn minimization in native clj (#106)

  • Multivariate

    • pure Clojure implementation of Nelder-Mead (#102)

• Native definite-integral numerics implementation, written as a series of computational essays:

  • Basics:

    • Riemann Sums, all the way up through efficient, incremental, "accelerated" versions of these easy-to-understand methods:
    • Midpoint method, same development but shorter since it reuses functional abstractions. Also incremental, efficient, accelerated
    • Trapezoid Method, same idea but for closed intervals.

  • Sequence Acceleration / Extrapolation Methods

    • Polynomial interpolation: the general thing that "richardson extrapolation" is doing below. Historically cool and used to accelerate arbitrary integration sequences
    • Rational Function extrapolation: used in bulirsch-stoer integration and ODE solving.
    • "Richardson extrapolation" is a special case, where we get more efficient by assuming that the x values for the polynomial interpolation go 1, 1/2, 1/4... and that we're extrapolating to 0.

  • Higher-order Calculus:

    • Numerical derivatives: derivatives using three kinds of central difference formulas... accelerated using Richardson extrapolation, with a nice technique for guarding against underflow.
    • Simpson's Method... fit a parabola to every slice. OR, "accelerate" the trapezoid method with one step of Richarsdson extrapolation!
    • Simpson's 3/8 Method: Same idea, but accelerate a sequence that triples its slices every iteration.
    • Boole's Rule: trapezoid method plus two steps of Richardson extrapolation. (Are you starting to see the pattern??)
    • Romberg Integration: midpoint OR trapezoid, with as many steps of Richardson extrapolation as we can take!
    • Milne's Rule, MIDPOINT method, one step of extrapolation!
    • Bulirsch-Stoer integration... midpoint or trapezoid, with rational function extrapolation, as many steps as we can handle AND some custom step sizes.

  • Combinators:

    • Variable Substitutions: implemented as functional wrappers that take an integrator and return a modified integrator.
    • Improper Integrals: a template for a combinator that enables infinite endpoints on any integrator, using variable substitution on an appropriate, tunable range.
    • Adaptive Integration: a combinator that turns any of the integrators above into an "adaptive" integrator that's able to focus in on difficult regions.

  • And finally, "Numerical Quadrature", the namespace/essay that ties it all together.

• sicmutils.numerical.compile uses SCI, the Small Clojure Interpreter, to generate compiled numerical code (#133)

• Implemented ODE solving using @littleredcomputer's odex-js library (#135)

Reader Literals

data_readers.cljc provides 3 new data reader literals:

• #sicm/ratio

Use this with a ratio literal, like #sicm/ratio 1/2, or with a string like #sicm/ratio "1/4". If the denominator is 1 this literal will return a js/BigInt in Clojurescript, or a Long in Clojure.

• #sicm/bigint

Use with a number literal, like, #sicm/bigint 10, or a string like #sicm/bigint "10000012" to generate a js/BigInt in Clojurescript, or a clojure.lang.BigInt in Clojure.

• #sicm/complex

Currently this only works with a string like #sicm/complex "1 + 2i". In the future it might work with a pair of (real, complex), like:

#sicm/complex [1 2]

Power Serious, Power Serious

The Power Series implementation in series.cljc received an overhaul. The implementation now follows Doug McIlroy's beautiful paper, "Power Series, Power Serious". Doug also has a 10-line version in Haskell on his website.

The API now offers two types:

• Series, which represents a generic infinite series of arbitrary values, and

• PowerSeries, a series that represents a power series in a single variable; in other words, a series where the nth entry is interpreted as the coefficient of $x^n$:

  $$[a b c d ...] == $a + bx + cx^2 + dx^3 + ...$$

series/series? responds true to both. series/power-series? only responds true to a PowerSeries.

To turn a PowerSeries into a Series, call it as a function with a single argument, or pass the series and one argument to series/value to evaluate the series using the above equation.

To turn a Series into a PowerSeries, call series/->function. None of the functions discussed below can mix series types; you'll have to do the conversion explicitly.

Each type supports the following generic operations:

• *, +, -, / between series and non-series
• g/negate, g/invert, g/sqrt, g/expt work as expected.
• g/add between series and non-series

PowerSeries additionally supports:

• g/exp, g/cos, g/sin, g/asin, g/tan
• g/partial-derivative, so PowerSeries works well with D

Each of these acts as function composition for the single variable function that the PowerSeries represents. If s is a PowerSeries that applies as (s x), (g/exp s) returns a series that represents (g/exp (s x)).

There are many more new methods (see the namespace for full documentation):

• starting-with renamed to series
• power-series, analogous series but generates a PowerSeries
• series* and power-series* let you pass an explicit sequence
• series/take removed in favor of clojure.core/take, since both series objects act as sequences
• generate takes an additional optional argument to distinguish between series and power series
• Series now implements more of v/Value
• new zero, one, identity constants
• constant returns a constant power series
• xpow generates a series representing a bare power of x
• ->function turns a Series into a PowerSeries
• value, fmap now handles both Series and PowerSeries
• (inflate s n) expands each term $x^i$ of s to $x^{in}$
• compose returns the functional composition of two PowerSeries
• revert returns the functional inverse of two PowerSeries
• integral returns a series representing the definite integral of the supplied PowerSeries, 0 => infinity (optionally takes an integration constant)

The namespace also provides many built-in PowerSeries instances:

• exp-series
• sin-series
• cos-series
• tan-series
• sec-series
• asin-series
• acos-series
• atan-series
• acot-series
• sinh-series
• cosh-series
• tanh-series
• asinh-series
• atanh-series
• log1+x-series
• log1-x-series
• binomial-series

And two Series (non-power):

• fib-series, the fibonacci sequence
• catalan-series, the Catalan numbers

Matrix Generic Operations

::matrix gained implementations for exp, cos, sin, asin, tan, acos, asin; these now return taylor series expansions of the operator, where multiplication is composition as before.

Operator Generics

Operator gained implementations for cos, sin, asin, tan, acos, asin; these now return taylor series expansions of the operator, where multiplication is composition as before.

[v0.21.1]

• Getting Github releases up to parity with the most recent release to Clojars.

[v0.10.0]

• Did some refactoring and one breaking rename (Struct became Structure, since we don't abbreviate other deftypes). This also marks the point of departure for working with Functional Differential Geometry.

[v0.9.8]

• This is the version that was current as of the talk @littleredcomputer gave at Clojure/west 2017, entitled "Physics in Clojure."