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Two proportional linears are not divided by their zero determinant - #1777
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Rafael-SOWNet merged 1 commit intoOct 5, 2026
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The recurrence for a negative power of one linear beside a power of another divides by the two linears' determinant, and declined where it was zero as written. Beside a multiple of the same linear, a + b x beside c a + c b x, it is b a c - a b c, zero only once its products are sorted, and the answer had no value anywhere. It is decided as a value now, and the integrand is left to the rules that answered it before the recurrence was added. Closes #1776. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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Closes #1776.
(a + b x)^(-3)/sqrt(c a + c b x)was answered on master with an expression that divides byb a c - a b c, which is zero, so it has no value at any point:4105b3bf(a + b x)^(-3)/sqrt(c a + c b x)-2/(5 b) (a + b x)^(-2) (c a + c b x)^(-1/2)1/(c (a + b x)^3)^(3/2), Rubi's 1.1.3.2:3412-2/(7 b c) sgn(a + b x) (c (a + b x))^(-1/2) (a + b x)^(-3)1/(c (a + b x)^3)^(5/2), 1.1.3.2:3413-2/(13 b c) sgn(a + b x) (c (a + b x))^(-3/2) (a + b x)^(-5)Each answer is differentiated back and compared with the integrand on both sides of the root of
a + b x.What changes. The recurrence #1758 added for a negative power of one linear beside a power of another divides by the two linears' determinant
D = b c' - a d', and declined whereDwas zero as written. Beside a multiple of the same linear it is zero only once the products in it are sorted. It is decided as a value now, withPartialFractions.IsZeroAsAValue, and the integrand is left to the rules that answered it before #1758; the rule for two linears beside each other already declines proportional ones, byAreProportionalAtSampledPoints.Tests:
LinearPowerRecurrenceIntegralTest.BesideAMultipleOfTheSameLinear, the three rows above, differentiated back at points on both sides of the root; master answers each with no value.Measured: the calculus and corpus tests pass on the head, and the library builds for
netstandard2.0. The change only declines where the determinant is zero as a value, which leaves the integrand to the rules before it.🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura