lift(f,R)
(Disambiguation: for division of matrices, which is thought of as lifting one homomorphism over another, see instead Matrix // Matrix. For lifting a map between modules to a map between their free resolutions, see extend.)
The ring R should be one of the base rings associated with the ring of f. An error is raised if f cannot be lifted to R.
The first example is lifting from the fraction field of R to R.
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Another use of lift is to take polynomials in a quotient ring and lift them to the polynomial ring.
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Elements may be lifted to any base ring, if such a lift exists.
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The functions lift and substitute are useful to move numbers from one kind of coefficient ring to another.
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A continued fraction method is used to lift a real number to a rational number, whereas promote uses the internal binary representation.
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For numbers and ring elements, an alternate syntax with ^ is available, analogous to the use of _ for promote.
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The object lift is a method function with options.