Rule: The contr from a pure curve Ga of 1/r(1,r-1) is

1/&*[1-t^i : i in [1,1,r,r]]
 * ( -b*t^{r+1} + a*t^3*((1-t^(r-2)) div (1-t)) * ((1-t^r) div (1-t)) );

where b = deg Ga (in units of 1/r^2) and deg_Ga(E1-E{r-1}) = 2*r*a - 2*b.

Comments: This is valid for r = 2, but then it doesn't involve a, and
simplifies to

 b* -t^3 / &*[1-t^i : i in [1,1,2,2]];

If E1-E{r-1} = Oh_Ga(al) then the term deg_Ga(E1-E{r-1}) is al * b 
and
 a = (al+2)*b / 2*r;
this is a problem in specifying a, b as integers: we have to take al and
b so that (al + 2)*B is divisible by 2*r.
The genus of Ga is present here: by adjunction
  K_Ga = K_Y + E1 + E{r-1}, so (for CY) 2g-2 = deg_Ga(E1+E{r-1}) = 2g-2.

In Magma

/* Contr of a 1/r(1,r-1) curve Ga is
a * t^3 * ((1-t^(r-2)) div (1-t)) * ((1-t^r) div (1-t))
- b * t^{r+1}
all over the standard denom 1/&*[1-t^i : i in [1,1,r,r]]. Note the funny way
of putting in the parameters: b = deg Ga and
 deg_Ga(E1-E{r-1}) = 2*r*a - 2*b.  */

function Ppc(r,a,b)
X := t^3*((1-t^(r-2)) div (1-t)) * ((1-t^r) div (1-t));
Y := -t^(r+1);
denom := &*[1-t^i : i in [1,1,r,r]];
return (a*X+b*Y)/denom;
end function;

===============

Rule: curve of 1/5(2,3) contr (a*X + b*Y)/[1,1,5,5] with
X := -t^3*((1-t^5) div (1-t))*(3-2*t+3*t^2);
Y := t^3*(1+t^2)*(1+t^2+t^4);

where deg Ga = b and deg_Ga (E2-E3) = 10*a - 4*b;

============

Rule: curve of 1/7(2,5) contr (a*X+b*Y)/[1,1,7,7] with
X := -t^3*((1-t^7) div (1-t))*(5-4*t+7*t^2-4*t^3+5*t^4);
Y := t^3*(1+t^2+t^4)*(1+t^2+t^4+t^6);
denom := &*[1-t^i : i in [1,1,7,7]];

where deg Ga = b and deg_Ga(E2-E5) = 14*a - 4*b?

============

[2,5,7,7,19,40],
d:=40; A:=[2,5,7,7,19]; B:=[[19,5,7,7]]; a:=-1; b:=1;
D := P(d,A) - PA(A) - Pb(B) - (a*X+b*Y)/denom;
 // 6*t^13+t^12+10*t^11+4*t^10+12*t^9+9*t^8+12*t^7+4*t^6+10*t^5+t^4+6*t^3
 // -X+Y; deg Ga = 1; E2 = Oh(-2); E5 = Oh(40-5-19) = Oh(16), E2-E5 = Oh(-18)
 
[2,5,7,7,19,40],
d:=40; A:=[2,5,7,7,19]; B:=[[19,5,7,7]];
D := P(d,A) - PA(A) - Pb(B);
 // 6*t^13+t^12+10*t^11+4*t^10+12*t^9+9*t^8+12*t^7+4*t^6+10*t^5+t^4+6*t^3
 // -X+Y; deg Ga = 1; E2 = Oh(-2); E5 = Oh(40-5-19) = Oh(16), E2-E5 = Oh(-18)

[2,5,7,7,21,42],
d:=42; A:=[2,5,7,7,21]; B:=[[5,1,2,2]];
D := P(d,A) - PA(A) - Pb(B);
 // -3*t^13-t^12-4*t^11-4*t^10-3*t^9-9*t^8-3*t^7-4*t^6-4*t^5-t^4-3*t^3
 // deg Ga = 2; E2 = Oh(-2), E5 = Oh(-5)

[2,5,7,7,21,42],
d:=42; A:=[2,5,7,7,21]; B:=[[5,1,2,2]]; a:=1; b:=2;
D := P(d,A) - PA(A) - Pb(B) - (a*X+b*Y)/denom;
 // -3*t^13-t^12-4*t^11-4*t^10-3*t^9-9*t^8-3*t^7-4*t^6-4*t^5-t^4-3*t^3
 // deg Ga = 2; E2 = Oh(-2), E5 = Oh(-5)

[3,4,7,7,7,28],
d:=28; A:=[3,4,7,7,7]; B := [[3,1,1,1]];
D := P(d,A) - PA(A) - Pb(B);
 // -2*t^12-2*t^11-8*t^8-2*t^5-2*t^4

[4,7,10,14,35,70],
d:=70; A:=[4,7,10,14,35]; B:=[[5,2,4,4]];
D := P(d,A) - PA(A) - Pb(B) - 70/(4*10*14)*Phalfc() + Pemb2(2);


[3,4,7,7,21,42],
d:=42; A:=[3,4,7,7,21]; B:=[[4,
D := P(d,A) - PA(A) - Pb(B);
 // does not have a tangent monomial at y

[3,4,7,7,18,39], // curve of 1/2 with emb 1/4(3,3,2) and 1/18(4,7,7)


[1,4,7,7,9,28], // doesn't actually have a curve of 1/7
d:=28; A:=[1,4,7,7,9]; B := [[9,4,7,7]];
D := P(d,A) - PA(A) - Pb(B);
  // if we pretend the denom is [1,1,7,7] then
  // 4*t^12 + 4*t^10 + 4*t^9 + 4*t^8 + 4*t^7 + 4*t^6 + 4*t^4

[1,10,11,33,55,110],
d := 110; A:=[1,10,11,33,55]; // emb 1/33(1,10,22)

[2,9,11,33,44,99], // emb 1/44
[2,9,11,33,53,108], // emb 1/33
[2,9,11,33,55,110], // emb 1/33(2,9,22)

[2,5,7,14,14,42], // curve of 1/7 with emb 3 x 1/14(2,5,7)
[2,5,7,14,26,54], // curve of 1/7 with emb 1 x 1/14(2,5,7) but also 1/26(5,7,14)
[2,5,14,14,35,70], // curve of 1/7 with emb 5 x 14/(2,5,7)

[5,5,8,12,18,48],
[5,5,17,18,45,90], // curve of 1/5(2,3) pure
d:=90; A:=[5,5,17,18,45]; B:=[[17,1,5,11],[9,5,5,8]];
D := P(d,A) - PA(A) - Pb(B);
 // -t^9 - t^8 - 4*t^6 - t^4 - t^3 = -X + Y
 // deg Ga = 2, E2 = Oh(-17), E3 = Oh(-18), E2-E3 = Oh(1), its deg = 2
 // a = 1; b := 2;

[2,3,3,5,5,18],
d := 18; A :=[2,3,3,5,5]; B:= [[3,2,2,2] : i in [1..6]];
D := P(d,A) - PA(A) - Pb(B);
 // 4*t^9 + t^8 + 6*t^7 + 4*t^6 + 6*t^5 + t^4 + 4*t^3 = 4X - Y
 // deg Ga = 1, E2 = Oh(-2), E3 = Oh(12), E2-E3 = Oh(-14), its deg = -14
 // b := 1, a:= -1;

[3,5,5,7,13,33],
d := 33; A:=[3,5,5,7,13]; B:=[[7,3,5,6],[13,3,5,5]];
D := P(d,A) - PA(A) - Pb(B);
 // 7*t^9 + 2*t^8 + 10*t^7 + 8*t^6 + 10*t^5 + 2*t^4 + 7*t^3
 // deg Ga = 1, E2 = Oh(-7), E3 = Oh(33-3-13) = Oh(17), E2-E3 = Oh(24), deg 24

[7,7,9,13,36,72],
d:=72; A:= [7,7,9,13,36]; B:=[[9,7,7,4],[9,7,7,4],[13,7,9,10]];
D := P(d,A) - PA(A) - Pb(B);
 // -6*t^13 - 3*t^12 - 9*t^11 - 6*t^10 - 12*t^9 - 13*t^8
 //               - 12*t^7 - 6*t^6 - 9*t^5 - 3*t^4 - 6*t^3

These check out Ppc

[1,6,7,7,15,36],
d:=36; A:=[1,6,7,7,15]; B:=[[15,1,7,7],[3,1,1,1]];
D := P(d,A) - PA(A) - Pb(B) - Ppc(7,2,1);
 // 2*t^13+4*t^12+6*t^11+8*t^10+10*t^9+9*t^8+10*t^7+8*t^6+6*t^5+4*t^4+2*t^3

[1,6,7,7,21,42],
d := 42; A:=[1,6,7,7,21]; B := []; B:=[[3,1,1,1]];
D := P(d,A) - PA(A) - Pb(B) - Ppc(7,1,2);
 // t^13+2*t^12+3*t^11+4*t^10+5*t^9+3*t^8+5*t^7+4*t^6+3*t^5+2*t^4+t^3