[Rafael-SOWNet]

Part of #233.

• An even power of the sine beside the secant, written in the cosine. Rubi's 4.5.1.3 sin(c + d x)^2/(a + b sec(c + d x)) ran past the corpus's budget. The half-angle substitution answered it, in 117,751 characters.
• Why. SolveByWritingARationalFunctionOfTheSecantInTheCosine wrote a rational function of the secant in the cosine beside the cosine itself, where the half angle had written cos(x)^2/(a + b sec(x)) in 117,409 characters. Beside the sine it declined, as a second function.
• The change. The sine stands there to even powers only, and sin(z)^(2k) is (1 - cos(z)^2)^k exactly, so it is now written so. (1 - cos(x)^2) cos(x)/(a cos(x) + b) is a polynomial over a linear in the cosine, which partial fractions answer in 969 characters. The cosine beside the cosecant goes into the sine the same way. An odd power of the complement still declines.

Input	master ef4150e	this branch
4.5.1.3:238 sin(c + d x)^2/(a + b sec(c + d x))	117,751 characters, 1.6 s, 0.54 GB	1,187 characters, 0.08 s, 0.03 GB
sin(x)^4/(a + b sec(x))	160,657 characters	1,729 characters
cos(x)^2/(a + b csc(x))	2,271 characters	994 characters

Chain against master ef4150e:

• The pocket of 7,606 rows, every 4.5 to 4.7 row and every row with a secant or cosecant in it, went from 7,605 to 7,606 solved.
• Every family's sample is unchanged.
• The one row that moved is 4.5.1.3:238, run alone: a timeout on master, solved here.
• 13,210 rows were compared for allocation, and none grew past 1.3x and 300 MB.

The library builds for netstandard2.0, net8.0 and net10.0. The suite is left to CI. The BREAKING-CHANGES lengths were measured on the branch, and the 2.5.0 column on a v2.5.0 build. Rebased onto e30f63f.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura