Enable numpy math functions to work with symbolic variables.

[soonho-tri]

#15038

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This change is 

[soonho-tri]

+@RussTedrake for feature-review, please.
+@EricCousineau-TRI for platform-review, please.

Reviewable status: LGTM missing from assignees RussTedrake(platform),EricCousineau-TRI(platform) (waiting on @EricCousineau-TRI and @RussTedrake)

[jwnimmer-tri]

FYI do you want Expression as well as Variable to have these methods?

[EricCousineau-TRI]

Reviewed 2 of 2 files at r1.
Reviewable status: 1 unresolved discussion, LGTM missing from assignees EricCousineau-TRI(platform),RussTedrake(platform) (waiting on @RussTedrake and @soonho-tri)

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bindings/pydrake/symbolic_py.cc, line 119 at r1 (raw file):

          },
          py::is_operator())
      // We add the following methods (exp, sqrt, sin, cos, tan, arcsin, arccos,

Ah, sorry; if you see the following, it may be possible to retarget the following method to do what you want:

drake/bindings/pydrake/symbolic_types_pybind.h

Lines 28 to 66 in da1d0d6

	// TODO(eric.cousineau): Per TODO in `symbolic_py.cc`, ensure that this binds
	// directly to the class, so it is the same as AutoDiff.
	// Adds math function overloads for Expression (ADL free functions from
	// `symbolic_expression.h`) for both NumPy methods and `pydrake.math`.
	// @param obj
	// This is used to register functions or overloads in either (a)
	// `pydrake.symbolic` or `pydrake.math`.
	template <typename PyObject>
	void BindSymbolicMathOverloads(PyObject* obj) {
	using symbolic::Expression;
	(*obj) // BR
	.def("log", &symbolic::log)
	.def("abs", &symbolic::abs)
	.def("exp", &symbolic::exp)
	.def("sqrt", &symbolic::sqrt)
	.def("pow",
	[](const Expression& base, const Expression& exponent) {
	return pow(base, exponent);
	})
	.def("sin", &symbolic::sin)
	.def("cos", &symbolic::cos)
	.def("tan", &symbolic::tan)
	.def("asin", &symbolic::asin)
	.def("acos", &symbolic::acos)
	.def("atan", &symbolic::atan)
	.def("atan2", &symbolic::atan2)
	.def("sinh", &symbolic::sinh)
	.def("cosh", &symbolic::cosh)
	.def("tanh", &symbolic::tanh)
	.def("min", &symbolic::min)
	.def("max", &symbolic::max)
	.def("ceil", &symbolic::ceil)
	.def("floor", &symbolic::floor)
	// TODO(eric.cousineau): This is not a NumPy-overridable method using
	// dtype=object. Deprecate and move solely into `pydrake.math`.
	.def("inv", [](const MatrixX<Expression>& X) -> MatrixX<Expression> {
	return X.inverse();
	});
	}

I'll see if I can do a quick PR

[soonho-tri]

FYI do you want Expression as well as Variable to have these methods?

@jwnimmer-tri , FYI, we've already handled the case:

[soonho-tri]

I'll see if I can do a quick PR

@EricCousineau-TRI , OK. Please ping me when you open your PR.

[EricCousineau-TRI]

Reviewable status: 1 unresolved discussion, LGTM missing from assignees EricCousineau-TRI(platform),RussTedrake(platform) (waiting on @EricCousineau-TRI and @RussTedrake)

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bindings/pydrake/symbolic_py.cc, line 119 at r1 (raw file):

Previously, EricCousineau-TRI (Eric Cousineau) wrote…

Ah, sorry; if you see the following, it may be possible to retarget the following method to do what you want:

drake/bindings/pydrake/symbolic_types_pybind.h

Lines 28 to 66 in da1d0d6

	// TODO(eric.cousineau): Per TODO in `symbolic_py.cc`, ensure that this binds
	// directly to the class, so it is the same as AutoDiff.
	// Adds math function overloads for Expression (ADL free functions from
	// `symbolic_expression.h`) for both NumPy methods and `pydrake.math`.
	// @param obj
	// This is used to register functions or overloads in either (a)
	// `pydrake.symbolic` or `pydrake.math`.
	template <typename PyObject>
	void BindSymbolicMathOverloads(PyObject* obj) {
	using symbolic::Expression;
	(*obj) // BR
	.def("log", &symbolic::log)
	.def("abs", &symbolic::abs)
	.def("exp", &symbolic::exp)
	.def("sqrt", &symbolic::sqrt)
	.def("pow",
	[](const Expression& base, const Expression& exponent) {
	return pow(base, exponent);
	})
	.def("sin", &symbolic::sin)
	.def("cos", &symbolic::cos)
	.def("tan", &symbolic::tan)
	.def("asin", &symbolic::asin)
	.def("acos", &symbolic::acos)
	.def("atan", &symbolic::atan)
	.def("atan2", &symbolic::atan2)
	.def("sinh", &symbolic::sinh)
	.def("cosh", &symbolic::cosh)
	.def("tanh", &symbolic::tanh)
	.def("min", &symbolic::min)
	.def("max", &symbolic::max)
	.def("ceil", &symbolic::ceil)
	.def("floor", &symbolic::floor)
	// TODO(eric.cousineau): This is not a NumPy-overridable method using
	// dtype=object. Deprecate and move solely into `pydrake.math`.
	.def("inv", [](const MatrixX<Expression>& X) -> MatrixX<Expression> {
	return X.inverse();
	});
	}

I'll see if I can do a quick PR

I've filed the following against this PR: soonho-tri#30

Didn't fully vet testing; please let me know if it's worth polishing this approach, and I can try to doc a bit more.

[EricCousineau-TRI]

Reviewable status: 1 unresolved discussion, LGTM missing from assignees EricCousineau-TRI(platform),RussTedrake(platform) (waiting on @RussTedrake and @soonho-tri)

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bindings/pydrake/symbolic_py.cc, line 119 at r1 (raw file):

Previously, EricCousineau-TRI (Eric Cousineau) wrote…

I've filed the following against this PR: soonho-tri#30

Didn't fully vet testing; please let me know if it's worth polishing this approach, and I can try to doc a bit more.

"fully vet testing" => I ran bazel test and it passes; however, I didn't add new tests

[EricCousineau-TRI]

Reviewable status: LGTM missing from assignees EricCousineau-TRI(platform),RussTedrake(platform), commits need curation (https://drake.mit.edu/reviewable.html#curated-commits) (waiting on @EricCousineau-TRI and @RussTedrake)

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bindings/pydrake/symbolic_py.cc, line 119 at r1 (raw file):

Previously, EricCousineau-TRI (Eric Cousineau) wrote…

"fully vet testing" => I ran bazel test and it passes; however, I didn't add new tests

OK Sweet! I'll push a few more fixes (including fixing CI).

[EricCousineau-TRI]

Reviewable status: 1 unresolved discussion, LGTM missing from assignees EricCousineau-TRI(platform),RussTedrake(platform), commits need curation (https://drake.mit.edu/reviewable.html#curated-commits) (waiting on @EricCousineau-TRI, @RussTedrake, and @soonho-tri)

a discussion (no related file):
nit Does this close above referenced issue? (at present, this only references it)

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[EricCousineau-TRI]

Reviewable status: 2 unresolved discussions, LGTM missing from assignees EricCousineau-TRI(platform),RussTedrake(platform), commits need curation (https://drake.mit.edu/reviewable.html#curated-commits) (waiting on @EricCousineau-TRI, @RussTedrake, and @soonho-tri)

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bindings/pydrake/symbolic_types_pybind.h, line 58 at r2 (raw file):

      .def("atan", &symbolic::atan, doc.atan.doc)
      .def("arctan2", &symbolic::atan2, doc.atan2.doc)
      .def("atan2", &symbolic::atan2, doc.atan2.doc)

Working: Significance of each separate overload is opaque. Trying to clarify with docs.

[soonho-tri]

-@EricCousineau-TRI
+@soonho-tri . With Eric's commit, I've only added the test cases. So I'll play the role of platform-reviewer.

Reviewable status: 2 unresolved discussions, LGTM missing from assignees soonho-tri(platform),RussTedrake(platform), commits need curation (https://drake.mit.edu/reviewable.html#curated-commits) (waiting on @EricCousineau-TRI, @RussTedrake, and @soonho-tri)

[EricCousineau-TRI]

Reviewable status: 1 unresolved discussion, LGTM missing from assignees soonho-tri(platform),RussTedrake(platform), commits need curation (https://drake.mit.edu/reviewable.html#curated-commits) (waiting on @EricCousineau-TRI, @RussTedrake, and @soonho-tri)

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bindings/pydrake/symbolic_types_pybind.h, line 58 at r2 (raw file):

Previously, EricCousineau-TRI (Eric Cousineau) wrote…

Working: Significance of each separate overload is opaque. Trying to clarify with docs.

OK Further docs will pollute scope of this PR. Opened #15041

[EricCousineau-TRI]

I've strictly timed out for this week; my suggestion is that this is a strict improvement. There's a mess underyling, but that can be resolved via follow-up such as #15041

Reviewable status: 1 unresolved discussion, LGTM missing from assignees soonho-tri(platform),RussTedrake(platform), commits need curation (https://drake.mit.edu/reviewable.html#curated-commits) (waiting on @EricCousineau-TRI, @RussTedrake, and @soonho-tri)

[RussTedrake]

Reviewed 3 of 4 files at r2, 1 of 1 files at r3.
Reviewable status: 2 unresolved discussions, LGTM missing from assignee soonho-tri(platform), commits need curation (https://drake.mit.edu/reviewable.html#curated-commits) (waiting on @soonho-tri)

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bindings/pydrake/symbolic_types_pybind.h, line 77 at r3 (raw file):

     // dtype=object. Deprecate and move solely into `pydrake.math`.
      .def(
          "inv",

nit: is this covered by a test? (I couldn't see it)?

[EricCousineau-TRI]

Reviewed 2 of 3 files at r4.
Reviewable status: 1 unresolved discussion, LGTM missing from assignee soonho-tri(platform), commits need curation (https://drake.mit.edu/reviewable.html#curated-commits) (waiting on @RussTedrake and @soonho-tri)

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bindings/pydrake/symbolic_types_pybind.h, line 77 at r3 (raw file):

Previously, RussTedrake (Russ Tedrake) wrote…

nit: is this covered by a test? (I couldn't see it)?

OK Yup! Actually, failures from prior revision was b/c I accidentally dropped this from the bindings 😅

[soonho-tri]

Reviewed 1 of 2 files at r1, 2 of 4 files at r2, 3 of 3 files at r4.
Reviewable status: 1 unresolved discussion, commits need curation (https://drake.mit.edu/reviewable.html#curated-commits) (waiting on @soonho-tri)

a discussion (no related file):

Previously, EricCousineau-TRI (Eric Cousineau) wrote…

nit Does this close above referenced issue? (at present, this only references it)

I'll check it after merging this PR.

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a discussion (no related file):
@EricCousineau-TRI , could you squash everything into a single commit and update this PR? Currently, if we squash this, I'm afraid I'll be the author of all the changes.

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[EricCousineau-TRI]

Reviewable status: 1 unresolved discussion (waiting on @soonho-tri)

a discussion (no related file):

Previously, soonho-tri (Soonho Kong) wrote…

@EricCousineau-TRI , could you squash everything into a single commit and update this PR? Currently, if we squash this, I'm afraid I'll be the author of all the changes.

Done!

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