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Expression of type Lambda

from the theory of proveit.physics.quantum.QPE

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, b
from proveit.logic import Equals, InSet
from proveit.numbers import Integer, frac, subtract
from proveit.physics.quantum.QPE import _delta_b, _phase, _two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = Lambda(b, Conditional(Equals(_delta_b, subtract(_phase, frac(b, _two_pow_t))), InSet(b, Integer)))
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())
b \mapsto \left\{\delta_{b} = \left(\varphi - \frac{b}{2^{t}}\right) \textrm{ if } b \in \mathbb{Z}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 22
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8, 9
6Literal
7ExprTuple22, 10
8Operationoperator: 11
operand: 22
9Operationoperator: 13
operands: 14
10Literal
11Literal
12ExprTuple22
13Literal
14ExprTuple15, 16
15Literal
16Operationoperator: 17
operand: 19
17Literal
18ExprTuple19
19Operationoperator: 20
operands: 21
20Literal
21ExprTuple22, 23
22Variable
23Operationoperator: 24
operands: 25
24Literal
25ExprTuple26, 27
26Literal
27Literal