But then necessarily the reductions modulo of and also make all non-leading terms vanish ( and cannot make their leading terms vanish ), since no other decompositions of are possible in, which is a unique factorization domain.
22.
This isomorphism makes the surreal numbers into a valued field where the valuation is the additive inverse of the exponent of the leading term in the Conway normal form, e . g ., ? ( ? ) =-1.
23.
Where, the original formulations by Dicke and Puthoff were inconsistent, using c ^ 4 / K or c ^ 4 / K ^ 2 in the leading term of the Lagrangian, rather than Depp's ( c / K ) ^ 4.
24.
The leading term of the product is the product of the leading terms of each factor ( this is true whenever one uses a monomial order, like the lexicographic order used here ), and the leading term of the factor is clearly.
25.
Where _ 2F _ 0 ( \ cdot, \ cdot;;-1 / x ) is a generalized hypergeometric series ( with 1 as leading term ), which generally converges nowhere but exists as a formal power series in 1 / " x ".
26.
The leading term of the product is the product of the leading terms of each factor ( this is true whenever one uses a monomial order, like the lexicographic order used here ), and the leading term of the factor is clearly.
27.
The leading term of the product is the product of the leading terms of each factor ( this is true whenever one uses a monomial order, like the lexicographic order used here ), and the leading term of the factor is clearly.
28.
The slant is reflected at every turn, such as anchors'use of leading terms like " pro-life " for abortion opponents and " pro-abortion " for supporters of reproductive rights and family planning that spares women from having to choose between childbirth and abortion.
29.
The algorithm terminates because it is consistently increasing the size of the monomial ideal generated by the leading terms of our set " F ", and Dickson's lemma ( or the Hilbert basis theorem ) guarantees that any such ascending chain must eventually become constant.
30.
A Gr�bner basis is termed " reduced " if the leading coefficient of each element of the basis is 1 and no monomial in any element of the basis is in the ideal generated by the leading terms of the other elements of the basis.
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