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 x.
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 is equal to x for x≥0, but not otherwise.
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This tells Simplify to make the assumption x>0, so that simplification can proceed.
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No automatic simplification can be done on this expression.
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If a and b 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 xi are elements of the domain dom |
| Reals | real numbers |
| Integers | integers |
| Primes | prime numbers |
Some domains used in assumptions.
This simplifies  assuming that x is a real number.
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This simplifies the sine assuming that n 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 sin (x), but not arcsin (x), is real when x is real.
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