logo

Expression of type InSet

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, c, f, j, m
from proveit.linear_algebra import LinMap, VecSum
from proveit.logic import CartExp, InSet
from proveit.numbers import Complex, one
from proveit.physics.quantum import Qmult, 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 = InSet(Qmult(Qmult(bra_varphi, alpha), VecSum(index_or_indices = sub_expr2, summand = Function(f, sub_expr2), condition = Function(Q, sub_expr2))), LinMap(CartExp(Complex, m), Complex))
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(\left(\langle \varphi \rvert \thinspace \alpha\right) \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]\right) \in \mathcal{L}\left(\mathbb{C}^{m}, \mathbb{C}\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: 11
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10, 20
8Operationoperator: 11
operands: 12
9Operationoperator: 13
operand: 19
10Operationoperator: 15
operands: 16
11Literal
12ExprTuple17, 18
13Literal
14ExprTuple19
15Literal
16ExprTuple20, 21
17Operationoperator: 22
operand: 25
18Variable
19Lambdaparameters: 30
body: 24
20Literal
21Variable
22Literal
23ExprTuple25
24Conditionalvalue: 26
condition: 27
25Variable
26Operationoperator: 28
operands: 30
27Operationoperator: 29
operands: 30
28Variable
29Variable
30ExprTuple31
31ExprRangelambda_map: 32
start_index: 33
end_index: 34
32Lambdaparameter: 38
body: 35
33Literal
34Variable
35IndexedVarvariable: 36
index: 38
36Variable
37ExprTuple38
38Variable