arnog
commented
2 months ago log of arbitrary base should already be handled through canonicalization.
Do those represent cases that don’t work even though they should or is it just a placeholder list of possible simplifications? Could you check which ones are actually necessary?
You could also submit a PR with corresponding test cases. The relevant file should be test/compute-engine/simplify.test.ts
andrew-murdza
\log_cshould be interpreted as a log with base cRelevant simplification rules
Undefined
{match:\log_c(a),replace:NaN,condition:c==1}{match:\log_c(a),replace:NaN,condition:c\le 0}\log_c(0)->NaNSimple
\log_c(1)->0\log_c(c)->1,\log_c(c^a)->aLog Properties
\log_c(ab)->\log_c(a)+\log_c(b)\log_c(\frac{a}{b})->\log_c(a)-\log_c(b)\log_c(\frac{1}{b})=-\log_c(b)\log_c(c^ab)->a+\log_c(b)\log_c(\frac{c^a}{b})->a-\log_c(b)\log_c(\frac{b}{c^a})->\log_c(b)-a\log_c(b^a)->a\log_c(b)Change of Base
\log_c(b)\ln(c)->\ln(b)\frac{\log_c(b)}{\log_d(b)}->\frac{\ln(d)}{\ln(c)}\log_{1/c}(b)->-\log_c(b)Base of C
c^{\log_c(a)}->ac^{b\log_c(a)}->a^bc^{\log_c(a)+b}->a\cdot c^bc^{\log_c(a)-b}->\frac{a}{c^b}c^{d\log_c(a)+b}->a^d\cdot c^bc^{\log_c(a)-b}->\frac{a^d}{c^b}c^{-\log_c(a)-b}->\frac{1}{a^dc^b}c^{-\log_c(a)+b}->\frac{b^c}{a^d}Infinity
{match:\log_c(\infty),replace:\infty,condition:c>1}{match:\log_c(\infty),replace:-\infty,condition:0<c<1}