Simplifying with Assumptions
| Simplify[expr,assum] | simplify expr with assumptions |
Simplifying with assumptions.
Mathematica does not automatically simplify this, since it is only true for some values of
.
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is equal to
for
, but not otherwise.
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This tells
Simplify to make the assumption
, so that simplification can proceed.
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No automatic simplification can be done on this expression.
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If
and
are assumed to be positive, the expression can however be simplified.
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Here is a simple example involving trigonometric functions.
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| Element[x,dom] | state that x is an element of the domain dom |
| Element[{x1,x2,...},dom] | state that all the  are elements of the domain dom |
| Reals | real numbers |
| Integers | integers |
| Primes | prime numbers |
Some domains used in assumptions.
This simplifies
assuming that
is a real number.
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This simplifies the sine assuming that
is an integer.
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With the assumptions given, Fermat's little theorem can be used.
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This uses the fact that
, but not
, is real when
is real.
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