realrank(...,Range=>...) -- can be assigned an interval

Synopsis

• Usage:

  realrank(F,Range=>(a,b))

  realrank(F,Range=>[a,b])

• Inputs:
  • F, a ring element, a binary form $F_u(x,y)\in \mathbb{Q}[u][x,y]$
  • a, a rational number, or an InfiniteNumber
  • b, a rational number, or an InfiniteNumber
• Outputs:
  • r, an integer, if the real rank of $F_u(x,y)$ is $r$ for all the values $u\in(a,b)$ or $u\in[a,b]$

Description

If the real rank of $F_u(x,y)$ is not constant over the interval, then an error message will be returned. The default value is (-infinity,infinity).

Further information

• Default value: (-infinity,infinity)
• Function: realrank -- compute the real rank
• Option key: Range -- can be assigned a integral interval

Functions with optional argument named Range:

• getPrimeWithRootOfUnity(...,Range=>...) -- see getPrimeWithRootOfUnity -- find a prime p with a primitive n-th root of unity r in ZZ/p
• realrank(...,Range=>...) -- can be assigned an interval