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Expression of type Equals

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, Function, IndexedVar, Q, Variable, alpha, beta, c, delta, f, gamma, j
from proveit.linear_algebra import VecSum
from proveit.logic import Equals
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 = Function(f, sub_expr2)
sub_expr4 = Function(Q, sub_expr2)
expr = Equals(Qmult(bra_varphi, alpha, VecSum(index_or_indices = sub_expr2, summand = sub_expr3, condition = sub_expr4), beta, ket_psi, gamma, bra_varphi, delta), VecSum(index_or_indices = sub_expr2, summand = Qmult(bra_varphi, alpha, sub_expr3, beta, ket_psi, gamma, bra_varphi, delta), condition = sub_expr4)).with_wrapping_at(1)
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())
\begin{array}{c} \begin{array}{l} \left(\langle \varphi \rvert \thinspace \alpha \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 \beta \thinspace \lvert \psi \rangle \thinspace \gamma \thinspace \langle \varphi \rvert \thinspace \delta\right) \\  = \left[\sum_{c_{1}, c_{2}, \ldots, c_{j}~|~Q\left(c_{1}, c_{2}, \ldots, c_{j}\right)}~\left(\langle \varphi \rvert \thinspace \alpha \thinspace f\left(c_{1}, c_{2}, \ldots, c_{j}\right) \thinspace \beta \thinspace \lvert \psi \rangle \thinspace \gamma \thinspace \langle \varphi \rvert \thinspace \delta\right)\right] \end{array} \end{array}
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()(1)('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 15
operands: 5
4Operationoperator: 9
operand: 8
5ExprTuple23, 18, 7, 20, 21, 22, 23, 24
6ExprTuple8
7Operationoperator: 9
operand: 12
8Lambdaparameters: 27
body: 11
9Literal
10ExprTuple12
11Conditionalvalue: 13
condition: 17
12Lambdaparameters: 27
body: 14
13Operationoperator: 15
operands: 16
14Conditionalvalue: 19
condition: 17
15Literal
16ExprTuple23, 18, 19, 20, 21, 22, 23, 24
17Operationoperator: 25
operands: 27
18Variable
19Operationoperator: 26
operands: 27
20Variable
21Operationoperator: 28
operand: 33
22Variable
23Operationoperator: 30
operand: 34
24Variable
25Variable
26Variable
27ExprTuple32
28Literal
29ExprTuple33
30Literal
31ExprTuple34
32ExprRangelambda_map: 35
start_index: 36
end_index: 37
33Variable
34Variable
35Lambdaparameter: 41
body: 38
36Literal
37Variable
38IndexedVarvariable: 39
index: 41
39Variable
40ExprTuple41
41Variable