[WIP] Add examples of usage of vector integration by friyaz · Pull Request #20021 · sympy/sympy

friyaz · 2020-08-30T21:28:31Z

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#19320

Brief description of what is fixed or changed

Add examples highlighting the usage of SymPy's vector integration functionality.

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#19320 

#### Brief description of what is fixed or changed
Add examples highlighting the usage of SymPy's vector integration functionality.

#### Other comments


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sympy-bot · 2020-08-30T21:28:40Z

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The following commits add new files:

fb5695b:
- doc/src/modules/vector/vector_integration.rst

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eric-wieser

Looks good so far.

codecov · 2020-08-31T18:18:23Z

Codecov Report

Merging #20021 into master will increase coverage by 0.005%.
The diff coverage is n/a.

@@              Coverage Diff              @@
##            master    #20021       +/-   ##
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+ Coverage   75.849%   75.854%   +0.005%     
=============================================
  Files          670       670               
  Lines       173699    173699               
  Branches     40978     40978               
=============================================
+ Hits        131750    131759        +9     
+ Misses       36209     36199       -10     
- Partials      5740      5741        +1

Upabjojr · 2020-08-31T20:49:40Z

+>>> sphere = ParametricRegion((r*sin(phi)*cos(theta),r*sin(phi)*sin(theta), r*cos(phi)),
+... (theta, 0, pi), (phi, 0, pi), (r, 0, 3))
+>>> vector_integrate(1, sphere)
+-18*pi


why is this result negative? I would indeed expect 18*pi, the volume of the half-sphere, as you have defined theta to reach pi (instead of 2*pi).

In ParametricIntegral class

variables = cls._bounds_case(parametricregion.limits) coeff = Matrix(parametricregion.definition).jacobian(variables).det() integrand = simplify(parametricfield*coeff) l = [(var, parametricregion.limits[var][0], parametricregion.limits[var][1]) for var in variables] result = integrate(integrand, *l)

The volume element requires calculating the jacobian. So the sign depends on the order of variables used in the calculation of jacobian. This order is determined by the bounds_case function which topologically sorts the parameters to remove the problem of interdependent bounds.

So in the current form, the order in which the bounds are defined at the initialization of ParametricRegion object does not matter in the calculation of integral. Because in the end, parameters ger sorted by bounds_case function. Is this correct? Or should the result depend on the order of parameters and the sorting should only take place when required?

For example,

sphere1 = ParametricRegion((r*sin(phi)*cos(theta),r*sin(phi)*sin(theta), r*cos(phi)),\ (theta, 0, pi), (phi, 0, pi), (r, 0, 3)) sphere2 = ParametricRegion((r*sin(phi)*cos(theta),r*sin(phi)*sin(theta), r*cos(phi)),\ (r, 0, 3), (theta, 0, pi), (phi, 0, pi))

In the present implementation, vector_integrate(1, sphere1) and vector_integrate(1, sphere2) returns result with same sign.
Is this desired or should the order matter?

Upabjojr · 2020-09-02T16:10:44Z

Any news?

Upabjojr · 2020-09-02T16:11:03Z

There are still some examples missing.

…xamples

Upabjojr · 2020-09-03T08:05:04Z

+
+Consider a triangular lamina 𝑅  with vertices (0,0), (0, 5), (5,0) and with density :math:`\rho(x, y) = xy\:kg/m^2`. Find the total mass.
+
+>>> triangle = ParametricRegion((x, y), (x, 0, 5), (y, 0, 5 - x))


does this work with the polygon object as well?

No. vector_integrate will perform line integral over the sides of the polygon instead of calculating the area enclosed.

OK, maybe that's an issue for some future work.

Yes. We can add new classes in geometry module for representing such regions.

I will open an issue for this then.

It would require an algorithm to decompose the polygon into triangles (or pyramids in the 3D case). Well, maybe for GSoC 2021 :)

Yes, for polygons it will be difficult. But I think adding a class to represent a triangular area will be easier.

…xamples

friyaz · 2020-09-04T14:08:32Z

(Copied from sympy/vector gitter room)

I still have some more things to add to this.

The functionality of finding rational parametrization from the implicit equation is not described anywhere except the docstring of the ParametricRegion class. I think it is a very important addition to SymPy and can be very helpful.
I think the examples will be more helpful if accompanied by figures.

Apart from these points, I think this PR is ready to merge. Perhaps, I will make these changes in a separate PR.

Initial draft of problems based on vector integration

fb5695b

friyaz marked this pull request as draft August 30, 2020 21:28

friyaz added Documentation GSoC vector labels Aug 30, 2020

Add example for permiter and volume calculation

3b2ba4d

friyaz requested a review from Upabjojr August 30, 2020 22:24

eric-wieser reviewed Aug 31, 2020

View reviewed changes

Comment thread doc/src/modules/vector/vector_integration.rst Outdated

Comment thread doc/src/modules/vector/vector_integration.rst Outdated

Comment thread doc/src/modules/vector/vector_integration.rst Outdated

hyperlink functions an dlcasses and fix doc tests

68e25b8

Upabjojr reviewed Aug 31, 2020

View reviewed changes

changed pi to 2*pi

e2802fb

friyaz added 2 commits September 2, 2020 22:27

Merge branch 'master' of https://github.com/sympy/sympy into vector-e…

8227a6e

…xamples

Add examples of flux calculation and total mass calculation

443cc3e

friyaz requested a review from Upabjojr September 2, 2020 21:03

Upabjojr reviewed Sep 3, 2020

View reviewed changes

friyaz mentioned this pull request Sep 3, 2020

Sign of integral of Parametricregion object #20044

Merged

friyaz added 2 commits September 4, 2020 18:59

Merge branch 'master' of https://github.com/sympy/sympy into vector-e…

9cd346c

…xamples

Correct sign of area

e062a64

friyaz requested review from Upabjojr and eric-wieser September 4, 2020 13:49

friyaz marked this pull request as ready for review September 4, 2020 17:09

Upabjojr merged commit e30ade0 into sympy:master Sep 5, 2020


		Consider a triangular lamina 𝑅 with vertices (0,0), (0, 5), (5,0) and with density :math:`\rho(x, y) = xy\:kg/m^2`. Find the total mass.

		>>> triangle = ParametricRegion((x, y), (x, 0, 5), (y, 0, 5 - x))

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friyaz commented Aug 30, 2020

References to other Issues or PRs

Brief description of what is fixed or changed

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Upabjojr commented Sep 2, 2020

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