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[poincare] Trigonometry: add rule arctan(1/x) = sign(x)*pi/2-arctan(x)

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This commit is contained in:
Émilie Feral
2018-12-18 18:04:18 +01:00
committed by Léa Saviot
parent c89fec872c
commit a02fd614ab
2 changed files with 19 additions and 2 deletions
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20
poincare/src/trigonometry.cpp
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@@ -5,6 +5,7 @@
#include <poincare/undefined.h>
#include <poincare/rational.h>
#include <poincare/multiplication.h>
#include <poincare/sign_function.h>
#include <poincare/subtraction.h>
#include <poincare/derivative.h>
#include <poincare/decimal.h>
@@ -252,7 +253,22 @@ Expression Trigonometry::shallowReduceInverseFunction(Expression & e, Context& c
}
}
// Step 3. Try finding an easy standard calculation reduction
// Step 3. Look for an expression of type "arctan(1/X), return sign(x)*Pi/2-arctan(x)
if (e.type() == ExpressionNode::Type::ArcTangent && e.childAtIndex(0).type() == ExpressionNode::Type::Power && e.childAtIndex(0).childAtIndex(1).type() == ExpressionNode::Type::Rational && e.childAtIndex(0).childAtIndex(1).convert<Rational>().isMinusOne()) {
Expression x = e.childAtIndex(0).childAtIndex(0);
Expression sign = SignFunction::Builder(x.clone());
Multiplication m0(Rational(1,2), sign, Constant(Ion::Charset::SmallPi));
sign.shallowReduce(context, angleUnit, target);
e.replaceChildAtIndexInPlace(0, x);
Addition a(m0);
e.replaceWithInPlace(a);
Multiplication m1(Rational(-1), e);
e.shallowReduce(context, angleUnit, target);
a.addChildAtIndexInPlace(m1, 1, 1);
return a.shallowReduce(context, angleUnit, target);
}
// Step 4. Try finding an easy standard calculation reduction
Expression lookup = Trigonometry::table(e.childAtIndex(0), e.type(), context, angleUnit, target);
if (!lookup.isUninitialized()) {
e.replaceWithInPlace(lookup);
@@ -266,7 +282,7 @@ Expression Trigonometry::shallowReduceInverseFunction(Expression & e, Context& c
* information on the parent which could later be a cosine, a sine or a tangent.
*/
bool letArcFunctionAtRoot = target == ExpressionNode::ReductionTarget::BottomUpComputation || parentIsDirectTrigonometry(e);
/* Step 4. Handle opposite argument: arccos(-x) = Pi-arcos(x),
/* Step 5. Handle opposite argument: arccos(-x) = Pi-arcos(x),
* arcsin(-x) = -arcsin(x), arctan(-x)= -arctan(x) *
*/
if (!letArcFunctionAtRoot) {

1
poincare/test/trigo.cpp
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@@ -511,6 +511,7 @@ QUIZ_CASE(poincare_trigo_simplify) {
assert_parsed_expression_simplify_to("atan(tan(1808))", "8", Preferences::AngleUnit::Degree);
assert_parsed_expression_simplify_to("atan(tan(-180/7))", "-180/7", Preferences::AngleUnit::Degree);
assert_parsed_expression_simplify_to("atan(R(3))", "60", Preferences::AngleUnit::Degree);
assert_parsed_expression_simplify_to("atan(1/x)", "(-2*atan(x)+sign(x)*P)/2", Preferences::AngleUnit::Degree);
// cos(arcsin)
assert_parsed_expression_simplify_to("cos(asin(x))", "R(1-x^2)", Preferences::AngleUnit::Degree);