▁matrix ▁operations ▁including ▁products , ▁in vers es , ▁etc . ▁statistical ▁computation ▁theorem ▁prov ing ▁and ▁ver ification ▁which ▁is ▁very ▁useful ▁in ▁the ▁area ▁of ▁experimental ▁mathematics ▁optimized ▁code ▁generation ▁ ▁In ▁the ▁above , ▁the ▁word ▁some ▁indicates ▁that ▁the ▁operation ▁cannot ▁always ▁be ▁performed . ▁ ▁Add itional ▁capabilities ▁Many ▁also ▁include : ▁a ▁programming ▁language , ▁allowing ▁users ▁to ▁implement ▁their ▁own ▁algorithms ▁arbitrary - prec ision ▁numeric ▁operations ▁exact ▁integer ▁arithmetic ▁and ▁number ▁theory ▁functionality ▁Edit ing ▁of ▁mathematical ▁expressions ▁in ▁two - dimensional ▁form ▁plot ting ▁graphs ▁and ▁paramet ric ▁plots ▁of ▁functions ▁in ▁two ▁and ▁three ▁dimensions , ▁and ▁anim ating ▁them ▁drawing ▁charts ▁and ▁diag rams ▁APIs ▁for ▁linking ▁it ▁on ▁an ▁external ▁program ▁such ▁as ▁a ▁database , ▁or ▁using ▁in ▁a ▁programming ▁language ▁to ▁use ▁the ▁computer ▁algebra ▁system ▁string ▁manip ulation ▁such ▁as ▁matching ▁and ▁searching ▁add - ons ▁for ▁use ▁in ▁applied ▁mathematics ▁such ▁as ▁physics , ▁bio in format ics , ▁computational ▁chem istry ▁and ▁packages ▁for ▁physical ▁computation ▁ ▁Some ▁include : ▁graph ic ▁production ▁and ▁editing ▁such ▁as ▁computer - generated ▁imag ery ▁and ▁signal ▁processing ▁as ▁image ▁processing ▁sound ▁synth esis ▁ ▁Some ▁computer ▁algebra ▁systems ▁focus ▁on ▁special ized ▁discipl ines ; ▁these ▁are ▁typically ▁developed ▁in ▁academ ia ▁and ▁are ▁free . ▁They ▁can ▁be ▁in efficient ▁for ▁numeric ▁operations ▁as ▁compared ▁to ▁numeric ▁systems . ▁ ▁Types ▁of ▁expressions ▁The ▁expressions ▁manip ulated ▁by ▁the ▁C AS ▁typically ▁include ▁polynomials ▁in ▁multiple ▁variables