# 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.
# import Expression classes needed to build the expression
from proveit import ExprRange, ExprTuple, Variable, e
from proveit.core_expr_types import Len
from proveit.numbers import Add, LessEq, Neg, one, three
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Len(operands = [LessEq(Add(Neg(_two_pow__t_minus_one), one), sub_expr2), LessEq(sub_expr2, _two_pow__t_minus_one), LessEq(_two_pow__t_minus_one, _two_pow__t_minus_one)]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, three)]))

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(\left(-2^{t - 1} + 1\right) \leq \left(e + 1\right), \left(e + 1\right) \leq 2^{t - 1}, 2^{t - 1} \leq 2^{t - 1}\right)|, |\left(1, 2, \ldots, 3\right)|\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1, 2
1Operationoperator: 4
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 7, 8
4Literal
5ExprTuple9
6Operationoperator: 12
operands: 10
7Operationoperator: 12
operands: 11
8Operationoperator: 12
operands: 13
9ExprRangelambda_map: 14
start_index: 36
end_index: 15
10ExprTuple16, 17
11ExprTuple17, 25
12Literal
13ExprTuple25, 25
14Lambdaparameter: 21
body: 21
15Literal
16Operationoperator: 30
operands: 19
17Operationoperator: 30
operands: 20
18ExprTuple21
19ExprTuple22, 36
20ExprTuple23, 36
21Variable
22Operationoperator: 34
operand: 25
23Variable
24ExprTuple25
25Operationoperator: 26
operands: 27
26Literal
27ExprTuple28, 29
28Literal
29Operationoperator: 30
operands: 31
30Literal
31ExprTuple32, 33
32Literal
33Operationoperator: 34
operand: 36
34Literal
35ExprTuple36
36Literal