from pmap import from_word, PMap
from evalmap import sfp, sfidx

def W(m, layers):
    return from_word(m, layers)[0]

def build_relations(t):
    """list of dicts: name, L, rhs [(coeff, map)], err: name of unknown block or None,
    errdim, errvec(fn) giving the error in L's coords as linear in unknowns."""
    one = t**0
    r0 = one/t
    rels = []
    strand = W(1, [])
    rels.append(dict(name="R1", L=W(1, [("cup",1),("X",0),("cap",1)]), rhs=[(one, strand)], err="a"))
    tau = W(2, [("T",0)])
    rels.append(dict(name="R15", L=W(2, [("X",0),("T",0)]), rhs=[(one, tau)], err="b"))
    rels.append(dict(name="R2", L=W(2, [("X",0),("X",0)]), rhs=[(one, W(2, []))], err="E2"))
    rels.append(dict(name="R25", L=W(3, [("X",0),("X",1),("T",0)]), rhs=[(one, W(3, [("T",1),("X",0)]))], err="E25"))
    rels.append(dict(name="R3", L=W(3, [("X",0),("X",1),("X",0)]), rhs=[(one, W(3, [("X",1),("X",0),("X",1)]))], err="E3"))
    rels.append(dict(name="Lol", L=W(0, [("cup",0),("T",0)]), rhs=[], err=None))
    rels.append(dict(name="Big", L=W(1, [("Ts",0),("T",0)]), rhs=[((t-2)/t, strand)], err=None))
    I = W(2, [("T",0),("Ts",0)])
    rels.append(dict(name="IH", L=I, rhs=[(one, I.rotated(1)), (r0, W(2, [])), (-r0, W(2, [("cap",0),("cup",0)]))], err=None))
    return rels