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[poincare] Power: fix infinite loop

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Factorizing 1+(8+sqrt(6))^(1/2)^(-1) on the same denominator would lead
to an infinite loop in Real mode (because (8+sqrt(6))^(1/2)^(-1) is not
simplified to (8+sqrt(6))^(-1/2))
This commit is contained in:
Émilie Feral
2019-04-19 17:56:26 +02:00
parent c4502ceab3
commit 4f4880de2a
2 changed files with 28 additions and 9 deletions
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34
poincare/src/power.cpp
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@@ -572,10 +572,22 @@ Expression Power::shallowReduce(Context & context, Preferences::ComplexFormat co
* This rule is not generally true: ((-2)^2)^(1/2) != (-2)^(2*1/2) = -2
* This rule is true if:
* - a > 0
* - in Real: when b and c are integers
* - in other modes: when c is integer
* (Warning: in real mode only c integer is not enough:
* ex: ((-2)^(1/2))^2 = unreal != -2)
* - c is an integer
*
* Warning 1: in real mode only c integer is not enough:
* ex: ((-2)^(1/2))^2 = unreal != -2
* We escape that case by returning 'unreal' if the a^b is complex.
*
* Warning 2: If we did not apply this rule on expressions of the form
* (a^b)^(-1), we would end up in infinite loop when factorizing an addition
* on the same denominator.
* For ex:
* 1+[tan(2)^1/2]^(-1) --> (tan(2)^1/2+tan(2)^1/2*[tan(2)^1/2]^(-1))/tan(2)^1/2
* --> tan(2)+tan(2)*[tan(2)^1/2]^(-1)/tan(2)
* --> tan(2)^(3/2)+tan(2)^(3/2)*[tan(2)^1/2]^(-1)/tan(2)^3/2
* --> ...
* Indeed, we have to apply the rule (a^b)^c -> a^(b*c) as soon as c is an
* integer.
*/
if (childAtIndex(0).type() == ExpressionNode::Type::Power) {
Power p = childAtIndex(0).convert<Power>();
@@ -584,11 +596,17 @@ Expression Power::shallowReduce(Context & context, Preferences::ComplexFormat co
bool cInteger = (childAtIndex(1).type() == ExpressionNode::Type::Rational
&& childAtIndex(1).convert<Rational>().integerDenominator().isOne());
if (aPositive || cInteger) {
// Check that the complex format is not Real or that b is an integer
bool bInteger = (p.childAtIndex(1).type() == ExpressionNode::Type::Rational && p.childAtIndex(1).convert<Rational>().integerDenominator().isOne());
if (aPositive || complexFormat != Preferences::ComplexFormat::Real || bInteger) {
return simplifyPowerPower(context, complexFormat, angleUnit, target);
/* If the complexFormat is real, we check that the inner power is defined
* before applying the rule (a^b)^c -> a^(b*c). Otherwise, we return
* 'unreal'. */
if (complexFormat == Preferences::ComplexFormat::Real) {
Expression approximation = p.approximate<float>(context, complexFormat, angleUnit);
if (approximation.type() == ExpressionNode::Type::Unreal) {
replaceWithInPlace(approximation);
return approximation;
}
}
return simplifyPowerPower(context, complexFormat, angleUnit, target);
}
}
// Step 11: (a*b*c*...)^r ?

3
poincare/test/power.cpp
View File

@@ -106,5 +106,6 @@ QUIZ_CASE(poincare_power_simplify) {
assert_parsed_expression_simplify_to("(-1)^(1/3)", "1/2+√(3)/2×𝐢");
assert_parsed_expression_simplify_to("R(-x)", "R(-x)");
assert_parsed_expression_simplify_to("√(x)^2", "x", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("√(x)^2", "√(x)^2", User, Radian, Real);
assert_parsed_expression_simplify_to("√(-3)^2", "unreal", User, Radian, Real);
assert_parsed_expression_simplify_to("1+((8+√(6))^(1/2))^-1+(8+√(6))^(1/2)", "(√(√(6)+8)+√(6)+9)/√(√(6)+8)", User, Radian, Real);
}