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Simplify Complex Arguments to Exp #1332

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Simplify Complex Arguments to Exp #1332

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1716ceb
Fixes #1330
ShikharJ Sep 27, 2017
cc81591
Minor Improvement
ShikharJ Oct 3, 2017
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28 changes: 28 additions & 0 deletions symengine/pow.cpp
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Expand Up @@ -164,6 +164,34 @@ RCP<const Basic> pow(const RCP<const Basic> &a, const RCP<const Basic> &b)
RCP<const Pow> A = rcp_static_cast<const Pow>(a);
return pow(A->get_base(), mul(A->get_exp(), b));
}
if (eq(*a, *E)) {
if (is_a<Mul>(*b)
and is_a_Complex(*down_cast<const Mul &>(*b).get_coef())) {
const map_basic_basic &dict = down_cast<const Mul &>(*b).get_dict();
if (dict.size() == 1) {
for (const auto &p : dict) {
if (eq(*p.first, *pi) and eq(*p.second, *one)) {
return add(cos(mul(mul(I, minus_one), b)),
mul(I, sin(mul(mul(I, minus_one), b))));
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This seems correct, as you can always do this transformation. The only question remaining is whether this transformation is only applied when it can simplify the exp(), and it seems it is.

It is probably possible to optimize this return statement further, using the information we know (i.e. not calling sin/cos at all), but that can be done later.

}
}
}
} else if (is_a<Add>(*b)) {
const umap_basic_num &dict = down_cast<const Add &>(*b).get_dict();
umap_basic_num new_dict;
RCP<const Number> coef = down_cast<const Add &>(*b).get_coef();
RCP<const Basic> s = one;
for (const auto &p : dict) {
if (eq(*p.first, *pi) and is_a_Complex(*p.second)) {
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Use is_a<Complex> to keep the consistency as above.

s = exp(mul(p.first, p.second));
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Can you take out the logic of mul to a new function and then call it from here so that we know if s was simplified that it is a number, else we can do Add::dict_add_term(new_dict, p.second, p.first);

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Can a call to exp be avoided here?

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@ShikharJ ShikharJ Oct 22, 2017 •
edited

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At the expense of code duplication it can be. I can't seem to think of another way.

} else {
Add::dict_add_term(new_dict, p.second, p.first);
}
}
return mul(s, make_rcp<const Pow>(
a, Add::from_dict(coef, std::move(new_dict))));
}
}
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We need to carefully benchmark these two if branches, before and after this PR. So the first if clause would run for something like E^(a*b). The second one for E^(a+b). Correct?

If so, then we need to benchmark these two things and similar things a lot.

return make_rcp<const Pow>(a, b);
}

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30 changes: 30 additions & 0 deletions symengine/tests/basic/test_arit.cpp
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Expand Up @@ -987,6 +987,36 @@ TEST_CASE("Pow: arit", "[arit]")
r1 = pow(mul(sqrt(mul(y, x)), x), i2);
r2 = mul(pow(x, i3), y);
REQUIRE(eq(*r1, *r2));

r1 = exp(mul(I, x));
r2 = pow(E, mul(I, x));
REQUIRE(eq(*r1, *r2));

r1 = exp(mul(I, pi));
r2 = pow(E, mul(I, pi));
REQUIRE(eq(*r1, *r2));

r1 = exp(mul(I, pi));
REQUIRE(eq(*r1, *minus_one));

r1 = exp(mul(mul(I, minus_one), pi));
REQUIRE(eq(*r1, *minus_one));

r1 = exp(div(mul(I, pi), integer(2)));
REQUIRE(eq(*r1, *I));

r1 = exp(mul(div(mul(I, pi), integer(2)), minus_one));
REQUIRE(eq(*r1, *mul(I, minus_one)));

r1 = div(exp(mul(mul(I, pi), x)), exp(x));
REQUIRE(r1->__str__() == "exp(-x + I*x*pi)");
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Can you change this test to checking that r1 is a Pow and that the base and exp are E and -x + I * x * pi respectively ?


r1 = exp(add(div(mul(I, pi), integer(2)), x));
r2 = mul(I, exp(x));
REQUIRE(eq(*r1, *r2));

r1 = exp(add(div(mul(I, pi), integer(10)), x));
REQUIRE(r1->__str__() == "exp(x)*(I*sin((1/10)*pi) + cos((1/10)*pi))");
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This is too complicated than it needs to be.

}

TEST_CASE("Log: arit", "[arit]")
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