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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, e, l
from proveit.logic import InSet
from proveit.numbers import Add, Exp, Interval, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one
In [2]:
# build up the expression from sub-expressions
expr = Lambda(l, Conditional(frac(one, Exp(l, two)), InSet(l, Interval(Add(e, one), subtract(_two_pow__t_minus_one, one)))))
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())
l \mapsto \left\{\frac{1}{l^{2}} \textrm{ if } l \in \{e + 1~\ldotp \ldotp~2^{t - 1} - 1\}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 14
body: 2
1ExprTuple14
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple31, 9
7Literal
8ExprTuple14, 10
9Operationoperator: 21
operands: 11
10Operationoperator: 12
operands: 13
11ExprTuple14, 23
12Literal
13ExprTuple15, 16
14Variable
15Operationoperator: 25
operands: 17
16Operationoperator: 25
operands: 18
17ExprTuple19, 31
18ExprTuple20, 28
19Variable
20Operationoperator: 21
operands: 22
21Literal
22ExprTuple23, 24
23Literal
24Operationoperator: 25
operands: 26
25Literal
26ExprTuple27, 28
27Literal
28Operationoperator: 29
operand: 31
29Literal
30ExprTuple31
31Literal