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Expression of type ExprTuple

from the theory of proveit.physics.quantum.algebra

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprRange, ExprTuple, Function, IndexedVar, Q, Variable, c, f, j
from proveit.linear_algebra import VecSum
from proveit.numbers import one
from proveit.physics.quantum import Qmult, bra_varphi, ket_psi
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [ExprRange(sub_expr1, IndexedVar(c, sub_expr1), one, j)]
sub_expr3 = VecSum(index_or_indices = sub_expr2, summand = Function(f, sub_expr2), condition = Function(Q, sub_expr2))
expr = ExprTuple(Qmult(bra_varphi, sub_expr3, ket_psi, bra_varphi), Qmult(Qmult(bra_varphi, sub_expr3, ket_psi), bra_varphi))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\langle \varphi \rvert \thinspace \left[\sum_{c_{1}, c_{2}, \ldots, c_{j}~|~Q\left(c_{1}, c_{2}, \ldots, c_{j}\right)}~f\left(c_{1}, c_{2}, \ldots, c_{j}\right)\right] \thinspace \lvert \psi \rangle \thinspace \langle \varphi \rvert, \left(\langle \varphi \rvert \thinspace \left[\sum_{c_{1}, c_{2}, \ldots, c_{j}~|~Q\left(c_{1}, c_{2}, \ldots, c_{j}\right)}~f\left(c_{1}, c_{2}, \ldots, c_{j}\right)\right] \thinspace \lvert \psi \rangle\right) \thinspace \langle \varphi \rvert\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1, 2
1Operationoperator: 6
operands: 3
2Operationoperator: 6
operands: 4
3ExprTuple8, 9, 10, 8
4ExprTuple5, 8
5Operationoperator: 6
operands: 7
6Literal
7ExprTuple8, 9, 10
8Operationoperator: 11
operand: 17
9Operationoperator: 13
operand: 18
10Operationoperator: 15
operand: 19
11Literal
12ExprTuple17
13Literal
14ExprTuple18
15Literal
16ExprTuple19
17Variable
18Lambdaparameters: 25
body: 20
19Variable
20Conditionalvalue: 21
condition: 22
21Operationoperator: 23
operands: 25
22Operationoperator: 24
operands: 25
23Variable
24Variable
25ExprTuple26
26ExprRangelambda_map: 27
start_index: 28
end_index: 29
27Lambdaparameter: 33
body: 30
28Literal
29Variable
30IndexedVarvariable: 31
index: 33
31Variable
32ExprTuple33
33Variable