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48 lines
1.2 KiB
Plaintext
48 lines
1.2 KiB
Plaintext
NAME
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minv - inverse of an integer modulo a specified integer
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SYNOPSIS
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minv(x, md)
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TYPES
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x integer
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md integer
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return integer
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DESCRIPTION
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If x and md are not relatively prime, zero is returned.
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Otherwise v = minv(x, md) is the canonical residue v modulo md
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for which v * x is congruent to 1 modulo md. The canonical
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residues modulo md are determined as follows by md and bits 0, 2
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and 4 of config("mod") (other bits are ignored).
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config("mod") md > 0 md < 0
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0 0 < v < md md < v < 0
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1 -md < v < 0 0 < v < -md
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4 0 < v < md 0 < v < -md
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5 -md < v < 0 md < v < 0
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16 -md/2 < v <= md/2 md/2 <= v < -md/2
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17 -md/2 <= v < md/2 md/2 < v <= -md/2
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20 -md/2 < v <= md/2 md/2 < v <= -md/2
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21 -md/2 <= v < md/2 md/2 <= v < -md/2
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EXAMPLE
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> c = config("mod", 0)
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> print minv(3,10), minv(-3,10), minv(3,-10), minv(-3,-10), minv(4,10)
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7 3 -3 -7 0
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> c = config("mod",16)
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> print minv(3,10), minv(-3,10), minv(3,-10), minv(-3,-10), minv(4,10)
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-3 3 -3 3 0
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LIMITS
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none
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LIBRARY
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NUMBER *qminv(NUMBER *x, NUMBER *md)
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SEE ALSO
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mod, pmod
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