# 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, Variable, e
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Add, Less, 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}")
sub_expr3 = Neg(sub_expr2)
expr = Equals(Len(operands = [LessEq(Add(Neg(_two_pow__t_minus_one), one), sub_expr3), Less(sub_expr3, sub_expr2), LessEq(sub_expr2, _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(-2^{t - 1} + 1\right) \leq \left(-\left(e + 1\right)\right), \left(-\left(e + 1\right)\right) < \left(e + 1\right), \left(e + 1\right) \leq 2^{t - 1}\right)| = |\left(1, 2, \ldots, 3\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: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9, 10
6Literal
7ExprTuple11
8Operationoperator: 15
operands: 12
9Operationoperator: 13
operands: 14
10Operationoperator: 15
operands: 16
11ExprRangelambda_map: 17
start_index: 41
end_index: 18
12ExprTuple19, 20
13Literal
14ExprTuple20, 26
15Literal
16ExprTuple26, 29
17Lambdaparameter: 24
body: 24
18Literal
19Operationoperator: 35
operands: 22
20Operationoperator: 39
operand: 26
21ExprTuple24
22ExprTuple25, 41
23ExprTuple26
24Variable
25Operationoperator: 39
operand: 29
26Operationoperator: 35
operands: 28
27ExprTuple29
28ExprTuple30, 41
29Operationoperator: 31
operands: 32
30Variable
31Literal
32ExprTuple33, 34
33Literal
34Operationoperator: 35
operands: 36
35Literal
36ExprTuple37, 38
37Literal
38Operationoperator: 39
operand: 41
39Literal
40ExprTuple41
41Literal