# MANNHEIM operations

Body:[A D], slide:[B C]

## Direct

FormulaScalesOperation
u2 [A,D] uD=>A(r)
[B,C] uC=>B(r)
u1/2 [D,A] uA=>D(r)
[C,B] uB=>C(r)

## Simple

FormulaScalesOperation
u2v2w-1 [A,B,C,D] wB->uD; vC=>A(r)
[B,A,C,D] uC->wA; vD=>B(r)
u2v2w-2 [A,C,D] wC->uD; vC=>A(r)
[B,C,D] uC->wD; vD=>B(r)
u2vw-1 [A,B,C] wB->vA; uC=>A(r)
[B,A,C] uC->wA; vA=>B(r)
[A,B,D] wB->uD; vB=>A(r)
[B,A,D] vB->wA; uD=>B(r)
u2vw-2 [B,D] vB->wD; uD=>B(r)
[B,A,C,D] uC->wD; vA=>B(r)
[A,B,C,D] wC->uD; vB=>A(r)
[A,C] wC->vA; uC=>A(r)
uvw-1/2 [D,B,C] wB->uD; vC=>D(r)
[C,A,D] uC->wA; vD=>C(r)
uvw-1 [D,C] wC->uD; vC=>D(r)
[B,A] uB->wA; vA=>B(r)
[C,D] uC->wD; vD=>C(r)
[A,B] wB->uA; vB=>A(r)
uvw-2 [B,A,D] uB->wD; vA=>B(r)
[A,B,C] wC->uA; vB=>A(r)
uv1/2w-1/2 [D,B] wB->uD; vB=>D(r)
[C,A,B,D] vB->wA; uD=>C(r)
[D,A,B,C] wB->vA; uC=>D(r)
[C,A] uC->wA; vA=>C(r)
uv1/2w-1 [D,B,C] wC->uD; vB=>D(r)
[D,A,C] wC->vA; uC=>D(r)
[C,B,D] vB->wD; uD=>C(r)
[C,A,D] uC->wD; vA=>C(r)
u1/2v1/2w-1/2 [D,A,B] wB->uA; vB=>D(r)
[C,A,B] uB->wA; vA=>C(r)
u1/2v1/2w-1 [D,A,B,C] wC->uA; vB=>D(r)
[C,A,B,D] uB->wD; vA=>C(r)

## Reduced to 2 variables

FormulaScalesOperation
u4v-1 [B,A,C,D] uC->vA; uD=>B(r)
[A,B,C,D] vB->uD; uC=>A(r)
u4v-2 [B,C,D] uC->vD; uD=>B(r)
[A,C,D] vC->uD; uC=>A(r)
u3v-1 [B,A,D] uB->vA; uD=>B(r)
[A,B,C] vB->uA; uC=>A(r)
[B,A,C] uC->vA; uA=>B(r)
[A,B,D] vB->uD; uB=>A(r)
u3v-2 [A,C] vC->uA; uC=>A(r)
[B,D] uB->vD; uD=>B(r)
[A,B,C,D] vC->uD; uB=>A(r)
[B,A,C,D] uC->vD; uA=>B(r)
u2v2 [A,C,D] 1C->uD; vC=>A(r)
[B,C,D] uC->1D; vD=>B(r)
u2v [B,A,C] uC->1D; vA=>B(r)
[A,B,C,D] vB->vD; uC=>A(r)
[B,A,C,D] vC->vA; uD=>B(r)
[B,A,C,D] uC->vA; vD=>B(r)
[A,B,D] 1C->uD; vB=>A(r)
[A,B,C,D] vB->uD; vC=>A(r)
[A,C] 1C->vA; uC=>A(r)
[B,D] vB->1D; uD=>B(r)
u2v-1/2 [D,B,C] vB->uD; uC=>D(r)
[C,A,D] uC->vA; uD=>C(r)
u2v-1 [B,A,D] 1C->vA; uD=>B(r)
[B,A,C] uC->vA; 1D=>B(r)
[B,D] vB->vD; uD=>B(r)
[A,B] vB->uA; uB=>A(r)
[B,A,C,D] uC->vD; vA=>B(r)
[C,D] uC->vD; uD=>C(r)
[A,C] vC->vA; uC=>A(r)
[D,C] vC->uD; uC=>D(r)
[A,B,C] vB->1D; uC=>A(r)
[A,B,D] vB->uD; 1C=>A(r)
[A,B,C,D] vC->uD; vB=>A(r)
[B,A] uB->vA; uA=>B(r)
u2v-2 [B,C,D] uC->vD; 1D=>B(r)
[B,D] 1C->vD; uD=>B(r)
[A,C] vC->1D; uC=>A(r)
[A,C,D] vC->uD; 1C=>A(r)
[A,B,C] vC->uA; uB=>A(r)
[B,A,D] uB->vD; uA=>B(r)
u3/2v-1/2 [D,A,B,C] vB->uA; uC=>D(r)
[C,A] uC->vA; uA=>C(r)
[D,B] vB->uD; uB=>D(r)
[C,A,B,D] uB->vA; uD=>C(r)
u3/2v-1 [C,B,D] uB->vD; uD=>C(r)
[D,B,C] vC->uD; uB=>D(r)
[C,A,D] uC->vD; uA=>C(r)
[D,A,C] vC->uA; uC=>D(r)
uv [C,D] uC->1D; vD=>C(r)
[B,A,D] vB->uA; uD=>B(r)
[A,B,C] uB->vA; uC=>A(r)
[B,A,C] uC->uA; vA=>B(r)
[B,A] uB->1D; vA=>B(r)
[A,B] 1C->uA; vB=>A(r)
[D,C] 1C->uD; vC=>D(r)
[A,B,D] uB->uD; vB=>A(r)
uv1/2 [D,A,C] 1C->vA; uC=>D(r)
[D,B,C] vB->uD; vC=>D(r)
[D,B,C] vB->vD; uC=>D(r)
[C,A,D] vC->vA; uD=>C(r)
[D,B] 1C->uD; vB=>D(r)
[C,B,D] vB->1D; uD=>C(r)
[C,A] uC->1D; vA=>C(r)
[C,A,D] uC->vA; vD=>C(r)
uv-1/2 [D,A,B] vB->uA; uB=>D(r)
[C,A,B] uB->vA; uA=>C(r)
[D,A,C] vC->vA; uC=>D(r)
[C,A] uC->vA; 1D=>C(r)
[C,A,D] 1C->vA; uD=>C(r)
[D,B] vB->uD; 1C=>D(r)
[D,B,C] vB->1D; uC=>D(r)
[C,B,D] vB->vD; uD=>C(r)
[D,B,C] vC->uD; vB=>D(r)
[C,A,D] uC->vD; vA=>C(r)
uv-1 [A,B,C] vC->vA; uB=>A(r)
[D,A,B,C] vC->uA; uB=>D(r)
[B,A] uB->vA; 1D=>B(r)
[C,A,B,D] uB->vD; uA=>C(r)
[A,B] vB->1D; uB=>A(r)
[C,D] uC->vD; 1D=>C(r)
[C,D] 1C->vD; uD=>C(r)
[D,C] vC->uD; 1C=>D(r)
[D,C] vC->1D; uC=>D(r)
[B,A,D] uB->vD; vA=>B(r)
[A,B] vB->uA; 1C=>A(r)
[B,A] 1C->vA; uA=>B(r)
[A,B,C] vC->uA; vB=>A(r)
[B,A,D] vB->vD; uA=>B(r)
uv-2 [A,C] vC->uA; 1C=>A(r)
[B,D] uB->vD; 1D=>B(r)
[A,B,C] vC->1D; uB=>A(r)
[B,A,D] 1C->vD; uA=>B(r)
u1/2v1/2 [D,B] uB->uD; vB=>D(r)
[C,A,B,D] vB->uA; uD=>C(r)
[D,A,B,C] uB->vA; uC=>D(r)
[C,A] uC->uA; vA=>C(r)
[C,A,B] uB->1D; vA=>C(r)
[D,A,B] 1C->uA; vB=>D(r)
u1/2v-1/2 [D,A,B,C] vC->uA; vB=>D(r)
[D,B] vB->1D; uB=>D(r)
[C,A,B,D] vB->vD; uA=>C(r)
[C,A,B,D] uB->vD; vA=>C(r)
[D,A,B,C] vC->vA; uB=>D(r)
[C,A,B] uB->vA; 1D=>C(r)
[D,A,B] vB->uA; 1C=>D(r)
[C,A] 1C->vA; uA=>C(r)
u1/2v-1 [C,A,D] 1C->vD; uA=>C(r)
[D,A,C] vC->uA; 1C=>D(r)
[C,B,D] uB->vD; 1D=>C(r)
[D,B,C] vC->1D; uB=>D(r)

## Reduced to 1 variable

FormulaScalesOperation
u4 [A,C,D] 1C->uD; uC=>A(r)
[B,C,D] uC->1D; uD=>B(r)
u3 [B,A,C] uC->1D; uA=>B(r)
[A,C] 1C->uA; uC=>A(r)
[A,B,D] 1C->uD; uB=>A(r)
[A,B,C,D] uB->uD; uC=>A(r)
[B,A,C,D] uC->uA; uD=>B(r)
[B,D] uB->1D; uD=>B(r)
u3/2 [D,B,C] uB->uD; uC=>D(r)
[C,B,D] uB->1D; uD=>C(r)
[C,A,D] uC->uA; uD=>C(r)
[C,A] uC->1D; uA=>C(r)
[D,A,C] 1C->uA; uC=>D(r)
[D,B] 1C->uD; uB=>D(r)
u-1/2 [C,B,D] uB->uD; 1D=>C(r)
[C,A,D] 1C->uD; uA=>C(r)
[D,A,C] uC->uA; 1C=>D(r)
[D,B] uB->1D; 1C=>D(r)
[C,A] 1C->uA; 1D=>C(r)
[D,B,C] uC->1D; uB=>D(r)
u-1 [B,A,D] 1C->uD; uA=>B(r)
[B,A] 1C->uA; 1D=>B(r)
[A,B,C] uC->1D; uB=>A(r)
[D,C] uC->1D; 1C=>D(r)
[B,D] uB->uD; 1D=>B(r)
[C,D] 1C->uD; 1D=>C(r)
[A,B] uB->1D; 1C=>A(r)
[A,C] uC->uA; 1C=>A(r)
u-2 [A,C] uC->1D; 1C=>A(r)
[B,D] 1C->uD; 1D=>B(r)

## Using search

FormulaScalesOperation
u4v-4 [A,B,C,D] vC->uD; |->D=B; |=>A
[B,A,C,D] uC->vD; |->A=C; |=>B
u2v-4 [A,B,C,D] vC->uA; |->D=B; |=>A
[B,A,C,D] uB->vD; |->A=C; |=>B

## Search reduced to 1 variable

FormulaScalesOperation
u-4 [B,A,C,D] 1C->uD; |->A=C; |=>B
[A,B,C,D] uC->1D; |->D=B; |=>A

## Search with inverted slide

FormulaScalesOperation
u4/3v4/3 [A,BI,CI,D] uCI->vD; |->D=BI; |=>A
[BI,A,CI,D] uCI->vD; |->A=CI; |=>BI
u4/3v2/3 [A,BI,D] vBI->uD; |->D=BI; |=>A
[A,BI,CI,D] uCI->vA; |->D=BI; |=>A
[BI,A,CI] uCI->vA; |->A=CI; |=>BI
[BI,A,CI,D] vBI->uD; |->A=CI; |=>BI
u2/3v2/3 [CI,A,D] uCI->vD; |->A=CI; |=>CI
[A,CI,D] uCI->vD; |->A=CI; |=>A
[D,BI,CI] uCI->vD; |->D=BI; |=>D
[A,BI,D] uBI->vA; |->D=BI; |=>A
[BI,A,CI] uBI->vA; |->A=CI; |=>BI
[BI,CI,D] uCI->vD; |->D=BI; |=>BI
u2/3v1/3 [CI,A,BI,D] vBI->uD; |->A=CI; |=>CI
[BI,A,CI,D] uCI->vA; |->D=BI; |=>BI
[A,BI,CI,D] vBI->uD; |->A=CI; |=>A
[A,CI] uCI->vA; |->A=CI; |=>A
[D,BI] vBI->uD; |->D=BI; |=>D
[BI,D] vBI->uD; |->D=BI; |=>BI
[D,A,BI,CI] uCI->vA; |->D=BI; |=>D
[CI,A] uCI->vA; |->A=CI; |=>CI
u1/2v1/4 [D,A,BI] vBI->uD; |->A=BI; |=>D
[D,A,BI,CI] uCI->vA; |->A=BI; |=>D
[CI,BI,D] vBI->uD; |->D=CI; |=>CI
[CI,A,BI] uCI->vA; |->A=BI; |=>CI
[D,BI,CI] vBI->uD; |->D=CI; |=>D
[D,A,CI] uCI->vA; |->D=CI; |=>D
[CI,A,BI,D] vBI->uD; |->A=BI; |=>CI
[CI,A,D] uCI->vA; |->D=CI; |=>CI
u1/3v1/3 [D,A,CI] uCI->vD; |->A=CI; |=>D
[A,BI,CI] uBI->vA; |->A=CI; |=>A
[CI,A,BI] uBI->vA; |->A=CI; |=>CI
[CI,BI,D] uCI->vD; |->D=BI; |=>CI
[D,A,BI] uBI->vA; |->D=BI; |=>D
[BI,A,D] uBI->vA; |->D=BI; |=>BI
u1/3v1/6 [CI,BI,D] vBI->uD; |->D=BI; |=>CI
[D,A,BI,CI] vBI->uD; |->A=CI; |=>D
[D,A,CI] uCI->vA; |->A=CI; |=>D
[CI,A,BI,D] uCI->vA; |->D=BI; |=>CI
u1/4v1/4 [D,A,BI,CI] uBI->vA; |->D=CI; |=>D
[CI,A,BI,D] uBI->vA; |->D=CI; |=>CI
[D,A,BI] uBI->vA; |->A=BI; |=>D
[CI,A,BI] uBI->vA; |->A=BI; |=>CI
u1/6v1/6 [CI,A,BI,D] uBI->vA; |->D=BI; |=>CI
[D,A,BI,CI] uBI->vA; |->A=CI; |=>D

## Search with inverted slide reduced to 1 variable

FormulaScalesOperation
u8/3 [A,BI,CI,D] uCI->uD; |->D=BI; |=>A
[BI,A,CI,D] uCI->uD; |->A=CI; |=>BI
u4/3 [A,BI,D] 1CI->uD; |->D=BI; |=>A
[BI,A,CI] uCI->1D; |->A=CI; |=>BI
[BI,A,CI] uBI->uA; |->A=CI; |=>BI
[A,CI,D] uCI->uD; |->A=CI; |=>A
[BI,A,CI,D] 1C->uD; |->A=CI; |=>BI
[A,BI,CI,D] uCI->1D; |->D=BI; |=>A
[BI,CI,D] uCI->uD; |->D=BI; |=>BI
[A,BI,D] uBI->uA; |->D=BI; |=>A
[D,BI,CI] uCI->uD; |->D=BI; |=>D
[A,BI,D] 1C->uD; |->D=BI; |=>A
[CI,A,D] uCI->uD; |->A=CI; |=>CI
[BI,A,CI,D] 1CI->uD; |->A=CI; |=>BI
u3/4 [CI,A,BI,D] uBI->uD; |->A=BI; |=>CI
[D,BI,CI] uBI->uD; |->D=CI; |=>D
[CI,BI,D] uBI->uD; |->D=CI; |=>CI
[D,A,BI] uBI->uD; |->A=BI; |=>D
[CI,A,BI] uCI->uA; |->A=BI; |=>CI
[CI,A,D] uCI->uA; |->D=CI; |=>CI
[D,A,CI] uCI->uA; |->D=CI; |=>D
[D,A,BI,CI] uCI->uA; |->A=BI; |=>D
u2/3 [A,CI,D] 1CI->uD; |->A=CI; |=>A
[CI,A] uCI->1D; |->A=CI; |=>CI
[CI,A,BI] uBI->uA; |->A=CI; |=>CI
[A,BI,D] 1CI->uA; |->D=BI; |=>A
[BI,D] 1CI->uD; |->D=BI; |=>BI
[CI,BI,D] uCI->uD; |->D=BI; |=>CI
[BI,A,CI] 1C->uA; |->A=CI; |=>BI
[BI,A,CI] uBI->1D; |->A=CI; |=>BI
[D,BI,CI] uCI->1D; |->D=BI; |=>D
[D,BI] 1C->uD; |->D=BI; |=>D
[D,A,BI] uBI->uA; |->D=BI; |=>D
[CI,A,D] 1CI->uD; |->A=CI; |=>CI
[BI,D] 1C->uD; |->D=BI; |=>BI
[A,CI] uCI->1D; |->A=CI; |=>A
[A,CI,D] 1C->uD; |->A=CI; |=>A
[A,BI,D] uBI->1D; |->D=BI; |=>A
[A,BI,CI] uBI->uA; |->A=CI; |=>A
[BI,CI,D] uCI->1D; |->D=BI; |=>BI
[D,BI] 1CI->uD; |->D=BI; |=>D
[BI,A,CI] 1CI->uA; |->A=CI; |=>BI
[BI,A,D] uBI->uA; |->D=BI; |=>BI
[A,BI,D] 1C->uA; |->D=BI; |=>A
[CI,A,D] 1C->uD; |->A=CI; |=>CI
[D,A,CI] uCI->uD; |->A=CI; |=>D
u1/3 [D,A,BI] 1C->uA; |->D=BI; |=>D
[A,BI,CI] uBI->1D; |->A=CI; |=>A
[BI,A,D] 1C->uA; |->D=BI; |=>BI
[D,A,CI] 1CI->uD; |->A=CI; |=>D
[BI,D] uBI->1D; |->D=BI; |=>BI
[A,CI] 1C->uA; |->A=CI; |=>A
[CI,BI,D] 1CI->uD; |->D=BI; |=>CI
[CI,A] 1C->uA; |->A=CI; |=>CI
[D,A,BI] 1CI->uA; |->D=BI; |=>D
[CI,A,BI] uBI->1D; |->A=CI; |=>CI
[A,CI] 1CI->uA; |->A=CI; |=>A
[BI,A,D] 1CI->uA; |->D=BI; |=>BI
[CI,BI,D] 1C->uD; |->D=BI; |=>CI
[D,A,CI] uCI->1D; |->A=CI; |=>D
[D,A,CI] 1C->uD; |->A=CI; |=>D
[D,A,BI,CI] uBI->uA; |->A=CI; |=>D
[D,BI] uBI->1D; |->D=BI; |=>D
[CI,BI,D] uCI->1D; |->D=BI; |=>CI
[CI,A] 1CI->uA; |->A=CI; |=>CI
[CI,A,BI,D] uBI->uA; |->D=BI; |=>CI
u1/4 [CI,BI,D] uBI->1D; |->D=CI; |=>CI
[CI,A,BI] 1C->uA; |->A=BI; |=>CI
[D,BI,CI] uBI->1D; |->D=CI; |=>D
[D,A,BI] 1C->uA; |->A=BI; |=>D
[D,A,CI] 1CI->uA; |->D=CI; |=>D
[CI,A,BI] 1CI->uA; |->A=BI; |=>CI
[CI,A,BI] uBI->1D; |->A=BI; |=>CI
[D,A,CI] 1C->uA; |->D=CI; |=>D
[D,A,BI] 1CI->uA; |->A=BI; |=>D
[D,A,BI] uBI->1D; |->A=BI; |=>D
[CI,A,D] 1C->uA; |->D=CI; |=>CI
[CI,A,D] 1CI->uA; |->D=CI; |=>CI
u1/6 [D,A,CI] 1C->uA; |->A=CI; |=>D
[CI,A,BI,D] 1C->uA; |->D=BI; |=>CI
[D,A,BI,CI] uBI->1D; |->A=CI; |=>D
[D,A,CI] 1CI->uA; |->A=CI; |=>D
[CI,A,BI,D] 1CI->uA; |->D=BI; |=>CI
[CI,BI,D] uBI->1D; |->D=BI; |=>CI

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