move some more loose files into git

.gitignore

@@ -1,7 +1,34 @@
 GRAPH*.pdf
 04-RATIONALS-EXAMPLE*.pdf
 
+ModernIntegration.pdf
+
+# a copy of Chapter 1, page 1
+wwtbam.pdf
+
+# directory with pythontex's autogenerated files
+pythontex-files-ModernIntegration
+
+# Auto-generated from 'maximacommon' blocks
+common.mac
+
+# Symlinks to auto-generated files
+maxima.mac
+chebyshev.mac
+sage.sage
+
+# LaTeX's comment package
+comment
+comment.sty
+
+# symlink to /home/baccala/texmf/fvextra/fvextra.sty
+fvextra.sty
+
+# symlink to /home/baccala/src/maxima-code/share/
+share
+
 # TeX litter
+ModernIntegration.pytxcode
 ModernIntegration.aux
 ModernIntegration.log
 ModernIntegration.out

CAS

@@ -0,0 +1,153 @@
+Comparison of open source computer algebra systems
+
+Axiom
+  doesn't use readline
+  builtin hyperdoc is way behind HTML
+  couldn't figure how to parse:
+    integrand := x*((x^2*exp(2*x^2)-log(x+1)^2)^2) / ((x+1)*(log(x+1)^2 - x^2*exp(2*x^2))^2)
+
+
+Maxima
+  uses LISP-style function definition syntax
+
+  MAXIMA function tex_displ(MLABEL %O14 EXPR)
+    - fetch tex-environment - either "" (strings) OR tex-environment property on car OR *tex-environment-default*
+    - print tex1(LABEL %O14) (minus 14 chars because of trailing \mathbb{false})
+    - then print env around tex1(EXPR)
+
+  MAXIMA function print(EXPR) calls displa for output
+
+
+Sage
+  struggling to do polynomial long division
+    calls Maxima or Singular to do this
+  implements algebraic closure of Q (QQbar)
+
+  + fix latex printing on power series
+  - subs should raise NotImplementedError if element not callable
+  - subs should work recursively on complicated rings
+  - option to specify how QQbar elements print
+  - can't type convert between two slightly different NumberRings:
+      Number Field in a with defining polynomial a^7 - 18
+      Number Field in a with defining polynomial y^7 - 18
+  - add map_coefficients method to Laurent series (Taylor, too?)
+
+
+Macaulay 2
+  doesn't implemente fraction fields over complicated (non-Z, non-Q) constant fields
+
+Singular
+  can't compute Riemann-Roch spaces in characteristic p
+  can compute Hamber-Noether expansions (can this be converted to a Puiseux expansion?)
+
+CoCoA
+  C++ library
+
+
+Macaulay 2 - Riemann-Roch space calculator (Noether-Brill algorithm ??)
+
+completeLinearSystemOnNodalPlaneCurve=method()
+completeLinearSystemOnNodalPlaneCurve(Ideal,List):=(J,D)->(
+     singJ:=saturate(ideal jacobian J+J);
+        -- adjoint ideal
+     H:=ideal (mingens ideal(gens intersect(singJ,D_0)%J))_(0,0);
+        -- a curve passing through singJ and D_0
+     E0:=((J+H):D_0):(singJ^2); -- residual divisor
+     if not(degree J *degree H - degree D_0 -2*degree singJ==degree E0)
+        then error"residual divisor of has wrong degree";
+     L1:=mingens ideal (gens truncate(degree H, intersect(E0,D_1,singJ)))%J;
+     h0D:=(tally degrees source L1)_{degree H}; -- h^0 O(D)
+     L:=L1_{0..h0D-1}; -- matrix of homogeneous forms, L/H =L(D) subset K(C)
+     (L,(gens H)_(0,0)))
+
+http://www2.macaulay2.com/Macaulay2/doc/Macaulay2-1.11/share/doc/Macaulay2/Macaulay2Doc/html/___Tutorial_co_sp__Divisors.html
+
+
+
+
+
+a=QQ['a'].0
+aRing = NumberField(a^2 + 1, 'a')
+
+b=QQ['b'].0
+bRing = NumberField(b^2 + 1, 'a')
+
+aRing is bRing
+
+aa=aRing.0
+bb=bRing.0
+
+bRing(aa)
+
+def ringmap(x):
+    # First map x from the polynomial ring down to its coefficent ring (a NumberField)
+    x = x.parent()(x)
+    # Then convert it to a polynomial and map to into numfield
+    return x.polynomial()(numfield.gens()[0])
+
+
+HOW TO CREATE A MAP BETWEEN TWO POLYNOMIAL RINGS INDUCED BY A MAP ON THEIR COEFFICIENTS
+
+R.<a> = QQ[]
+aRing = NumberField(a^2 + 1, 'a')
+R.<b> = QQ[]
+bRing = NumberField(b^2 + 1, 'a')
+
+aRing2 = aRing['x']
+bRing2 = bRing['x']
+
+h = aRing.hom(bRing.gens())
+
+h2 = aRing2.hom(h, bRing2)
+
+DOESN'T WORK FOR LAURENT SERIES
+
+
+
+BUG REPORT TO SHOW HOW SINGULAR RETURNS RESULTS IN WRONG FIELD
+
+R.<b> = QQ[]
+S = NumberField(b^7 - 18, 'a')
+
+R.<x,y> = S[]
+f = x + y
+
+singular.lib('hnoether.lib')
+hne = f._singular_().hnexpansion().sage()
+
+hne[0][0].base_ring() is f.parent()
+
+
+
+SAGE - SINGULAR IDEALS
+
+rings/polynomial/multi_polynomial_ideal.py
+  lines 558-592
+  create Singular ideal
+  lift generators into parent ring before str-ifying them for Singular
+
+interfaces/singular.py
+  lines 1957-1959
+  converts Singular ideal to sage ideal
+
+   1958             R = R or self.sage_global_ring()
+   1959             return R.ideal([p.sage_poly(R) for p in self])
+
+  if R is a quotient ring,
+    p.sage_poly(R) can't be lifted into the base ring
+
+  sage_poly:
+
+   1779             p = MPolynomial_polydict(R,PolyDict(sage_repr,force_int_exponents=False,force_etuples=False))
+   1780             if isinstance(R, MPolynomialRing_polydict):
+   1781                 return p
+   1782             else:
+   1783                 return QuotientRingElement(R,p,reduce=False)
+
+  what we get back is a QuotientRingElement containing an MPolynomial_polydict
+
+  self.sage_global_ring() will return a quotient ring different from the one we started with
+    its generators will be named 'x', 'y', 'z', instead of 'xbar', 'ybar', 'zbar'
+
+  subs doesn't work because _call_ isn't defined on QuotientRingElement's
+    (subs in RingElement returns self if _call_ isn't defined)

cyclotomic.gp

@@ -0,0 +1,34 @@
+#!/bin/sh
+#
+# gnuplot script to plot roots of an equation
+
+equation=$1
+if [ "x$equation" = "x" ]; then equation="z**6-1"; fi
+
+/usr/bin/gnuplot -geometry 500x500 -persist <<EOF
+#cat > cyclo.out <<EOF
+
+unset ztics
+set ticslevel 0
+set grid
+set zeroaxis lt 3
+
+min(a,b) = a>b ? b : a
+
+set isosamples 500,500
+
+set view 0,0
+
+set key off
+set size 1.4,1.4
+set origin -0.2,-0.2
+
+strength = 1.0
+poly(z) = (strength * ($equation))
+
+splot [-2:2] [-2:2] [5:100] min(abs(1/poly(x+{0,1}*y)),10)
+
+bind Up "strength = strength * 2; replot"
+bind Down "strength = strength / 2; replot"
+
+EOF

references/maxima-integral

@@ -0,0 +1,157 @@
+A bunch of responses:
+
+1. Thanks for providing a brief way of producing this error message.
+2. If you really want an answer, you could try
+
+integrate_use_rootof:true;
+
+integrate(1/(x^(5/2)+3*x^(1/3)),x);
+
+though I'm not sure the answer returned is correct or
+even sensible.
+
+It returns
+6*lsum(log(x^(1/6)-%r1)/(13*%r1^9),%r1,rootsof(x^(13/6)+3))
+
+Mathematica produces an answer, but one which is quite large.
+Wolfram Alpha produces an answer that is different but is
+also large, and runs out of time, it seems, in analyzing the
+expression.  Incidentally, it apparently allows the Maxima syntax :)
+
+I'm not sure the answer is correct or even sensible. The
+Mathematica system 10 could not simplify the derivative back
+to the input, at least not before I lost patience.
+
+
+
+3. My understanding of algebraic:true  is that it uses
+only roots of integers  (absent in your expression)
+%i (also absent),  and tellrat() info  (also absent).
+So setting algebraic to true is maybe not the right thing to do.
+
+Introducing  both sqrt(x) and x^(1/3) by a single algebraic
+extension of degree 6  is possible via tellrat.  I'm not
+sure this gets you to where you want.
+
+Or even if you really want this integral or are just poking at Maxima.
+
+4. If you really want to try to patch this bug in the handling of
+algebraic:true,
++ integrate + ratsimp,  not by fixing the bug, but by catching it in a
+different
+place, you can look at code in src/rat3a.lisp  where you can see that the
+polynomial division  in the function pquotient, at some point says, in
+effect,
+HEY!  you want me to divide exactly -- that's what pquotient does -- but
+the remainder is not zero.  There's no bug in pquotient, but there is a bug
+in someone who called it on bad argumemtns.   (This is probably because
+the GCD routine in use  fails when there are algebraically dependent
+indeterminates,  but this handling of algebraics is touchy. maybe because
+of comment 1. (thanks) someone can find this???   Anyway, this
+error-catch of the throw in pquotient is what you would have to change, so
+that
+it doesn't just vomit all the way to the top, but to some other err-catch.
+Maybe you can figure out enough from the comments and the code to
+do this.   The main body of code (but not all the comments) are almost
+50 years old,  circa 1966 I think.
+
+5. I am not sure what you mean by "throw to the outside" and how this makes
+life easier.  Perhaps you are resisting the "easy" way -- which is to use
+the Maxima  read-meval-print loop to call your functionality --   and
+calling
+Maxima  via some other language at the end of a pipe?
+(Why easy?   load into Maxima some lisp function from a file foo, by
+load("c:/..../foo.lisp");
+
+and in the file foo.lisp
+
+(defun $sherfgen(x)  (call_whatever_you_want_next    x))
+
+;; call_whatever .... can link to fortran, python, jscript, java, most any
+ windows dll, typical unix .o files, libraries etc
+
+And the load()  command can be put into a maxima initialization file so
+it is loaded up without user attention.
+
+
+Anyway. I  hope this info is useful, and you take the opportunity to learn
+more lisp and
+Maxima stuff.
+
+RJF
+
+
+On Mon, Sep 7, 2015 at 12:54 AM, David Scherfgen <d.scherfgen at googlemail.com
+> wrote:
+
+> Hello,
+>
+> the following integral results in an error "quotient by zero":
+>
+> integrate(ev(ratsimp(1/(x^(5/2)+3*x^(1/3))),algebraic),x);
+>
+> Unfortunately, I can't catch the error using errcatch. It goes right
+> through it, i.e. the whole evaluation is aborted, and I don't get any
+> result (usually, errcatch would give me an empty list if it caught an
+> error).
+>
+> I've had a similar problem with questions being asked by Maxima - there is
+> no official way to intercept them. This is really bad if you run Maxima
+> "automatedly" - without anybody being there to answer questions.
+>
+> But luckily, there is Robert Dodier's noninteractive package that
+> re-defines the Maxima functions that are responsible for asking those
+> questions. The re-defined functions don't ask the questions, but throw
+> them, so that it can be caught from the outside.
+>
+> I tried to do something similar with the function that's responsible for
+> generating the error, the function merror in merror.lisp.
+>
+> This is my attempt at it:
+>
+> ; If this is enabled, errors will be intercepted and thrown.
+> (defmvar $no_errors t)
+>
+> ; A wrapper around MERROR in merror.lisp.
+> (defvar *real-merror* (symbol-function 'merror))
+> (defun merror (sstring &rest l)
+>   (if $no_errors
+>     (meval `(($throw) '(($merror) ,sstring ,@ l)))
+>     (apply *real-merror* sstring l)))
+>
+> In a simple test case, it seems to work:
+>
+> (%i1) catch(1/0);
+> (%o1) merror("expt: undefined: 0 to a negative exponent.")
+>
+> It throws the error instead of aborting the evaluation, just as I want.
+>
+> But in my original problem, it doesn't work, but crashes Maxima instead:
+>
+> (%i1) catch(integrate(ev(ratsimp(1/(x^(5/2)+3*x^(1/3))),algebraic),x));
+> Maxima encountered a Lisp error:
+>  Condition in MEVAL [or a callee]: INTERNAL-SIMPLE-ERROR: Bind stack
+> overflow.
+> Automatically continuing.
+> To enable the Lisp debugger set *debugger-hook* to nil.
+>
+> Unfortunately, my LISP knowledge is basically nonexistent.
+>
+> Does anyone of you know why this doesn't work? Why can't errcatch catch
+> the error in the first place? Is there something wrong with my merror
+> wrapper?
+>
+> Thanks for any help!
+>
+> Best regards,
+> David
+>
+>
+> ------------------------------------------------------------------------------
+>
+> _______________________________________________
+> Maxima-discuss mailing list
+> Maxima-discuss at lists.sourceforge.net
+> https://lists.sourceforge.net/lists/listinfo/maxima-discuss
+>
+>