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Expression of type Lambda

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 Conditional, Lambda, i, n
from proveit.core_expr_types import x_i
from proveit.logic import InSet
from proveit.numbers import Interval, one
from proveit.physics.quantum import Bra, Ket, Qmult
In [2]:
# build up the expression from sub-expressions
expr = Lambda(i, Conditional(Qmult(Ket(x_i), Bra(x_i)), InSet(i, Interval(one, n))))
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())
i \mapsto \left\{\lvert x_{i} \rangle \thinspace \langle x_{i} \rvert \textrm{ if } i \in \{1~\ldotp \ldotp~n\}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 21
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8, 9
6Literal
7ExprTuple21, 10
8Operationoperator: 11
operand: 16
9Operationoperator: 12
operand: 16
10Operationoperator: 14
operands: 15
11Literal
12Literal
13ExprTuple16
14Literal
15ExprTuple17, 18
16IndexedVarvariable: 19
index: 21
17Literal
18Variable
19Variable
20ExprTuple21
21Variable