SUBST: Difference between revisions
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Substitute the equation or the list of equations into the expression. All substitutions will be done in parallel, which means that after substituting a list of equations like <code>x = y; y = z</code> the expression might still contain the variable <code>y</code>. In this case you need to use [[SUBSTC]] instead. | Substitute the equation or the list of equations into the expression/equation. All substitutions will be done in parallel, which means that after substituting a list of equations like <code>x = y; y = z</code> the expression might still contain the variable <code>y</code>. In this case you need to use [[SUBSTC]] instead. | ||
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Revision as of 19:17, 29 June 2017
Syntax
SUBST ( expression | equation , equation | equation list )
Implemented in iMath since version 2.2.0 or earlier.
Explanation
Substitute the equation or the list of equations into the expression/equation. All substitutions will be done in parallel, which means that after substituting a list of equations like x = y; y = z the expression might still contain the variable y. In this case you need to use SUBSTC instead.
Example
@eq:cubic@ EQDEF x^3 + a x^2 + b x + c = 0
@eq:tsch3@ EQDEF y = x + {a over 3}
EQDEF COLLECT(SIMPLIFY(SUBSTC(@eq:cubic@, SOLVE(@eq:tsch3@, x, 1)),"expand"), y)
This will perform the Tschirnhaus transformation on the cubic equation, reducing it to the depressed form y^3 + p y + q.