logo

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, beta, c, delta, f, gamma, j
from proveit.core_expr_types import Len
from proveit.linear_algebra import VecSum
from proveit.logic import Equals
from proveit.numbers import five, one
from proveit.physics.quantum import bra_varphi
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)]
expr = Equals(Len(operands = [beta, gamma, delta, bra_varphi, VecSum(index_or_indices = sub_expr2, summand = Function(f, sub_expr2), condition = Function(Q, sub_expr2))]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, five)]))
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(\beta, \gamma, \delta, \langle \varphi \rvert, \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)| = |\left(1, 2, \ldots, 5\right)|
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.()()('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: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9, 10, 11, 12
6Literal
7ExprTuple13
8Variable
9Variable
10Variable
11Operationoperator: 14
operand: 20
12Operationoperator: 16
operand: 21
13ExprRangelambda_map: 18
start_index: 30
end_index: 19
14Literal
15ExprTuple20
16Literal
17ExprTuple21
18Lambdaparameter: 35
body: 35
19Literal
20Variable
21Lambdaparameters: 27
body: 22
22Conditionalvalue: 23
condition: 24
23Operationoperator: 25
operands: 27
24Operationoperator: 26
operands: 27
25Variable
26Variable
27ExprTuple28
28ExprRangelambda_map: 29
start_index: 30
end_index: 31
29Lambdaparameter: 35
body: 32
30Literal
31Variable
32IndexedVarvariable: 33
index: 35
33Variable
34ExprTuple35
35Variable