Promote

[pzinn]

This PR addresses some of the issues raised in #3184. before:

i1 : R=QQ[x]

o1 = R

o1 : PolynomialRing

i2 : S=R[y]

o2 = S

o2 : PolynomialRing

i3 : 1/x+1/y
stdio:3:3:(3): error: expected pair to have a method for '+'

i4 : matrix{{1/x}}*matrix{{1/y}}
stdio:4:13:(3): error: maps over incompatible rings

i5 : promote(1/x_R,frac S)
stdio:5:7:(3): error: no method found for applying promote to:
                   1
     argument 1 :  - (of class frac R)
                   x
     argument 2 :  frac S

i6 : lift(1/x_S,frac R)
stdio:6:4:(3): error: no method found for applying lift to:
                   1
     argument 1 :  - (of class frac S)
                   x
     argument 2 :  frac R

and

i1 : R=QQ[x]

o1 = R

o1 : PolynomialRing

i2 : T=R**QQ[z]

o2 = T

o2 : PolynomialRing

i3 : x_R*z
stdio:3:3:(3): error: expected pair to have a method for '*'

after:

i1 : R=QQ[x]

o1 = R

o1 : PolynomialRing

i2 : S=R[y]

o2 = S

o2 : PolynomialRing

i3 : 1/x+1/y

     y + x
o3 = -----
      x*y

o3 : frac S

i4 : matrix{{1/x}}*matrix{{1/y}}

o4 = | 1/xy |

                    1             1
o4 : Matrix (frac S)  <-- (frac S)

i5 : promote(1/x_R,frac S)

     1
o5 = -
     x

o5 : frac S

i6 : lift(1/x_S,frac R)

     1
o6 = -
     x

o6 : frac R

and

i1 : R=QQ[x]

o1 = R

o1 : PolynomialRing

i2 : T=R**QQ[z]

o2 = T

o2 : PolynomialRing

i3 : x_R*z

o3 = x*z

o3 : T

In particular it introduces a new method setupPromote which makes it easy to (automatically) promote from A -> B given a map f: A -> B.