# 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 e
from proveit.core_expr_types import Len
from proveit.numbers import Add, LessEq, Neg, one
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

In [2]:
# build up the expression from sub-expressions
expr = Len(operands = [LessEq(Add(Neg(_two_pow__t_minus_one), one), sub_expr1), LessEq(sub_expr1, _two_pow__t_minus_one), LessEq(_two_pow__t_minus_one, _two_pow__t_minus_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())

|\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)|

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',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4, 5
3Operationoperator: 8
operands: 6
4Operationoperator: 8
operands: 7
5Operationoperator: 8
operands: 9
6ExprTuple10, 11
7ExprTuple11, 17
8Literal
9ExprTuple17, 17
10Operationoperator: 22
operands: 12
11Operationoperator: 22
operands: 13
12ExprTuple14, 28
13ExprTuple15, 28
14Operationoperator: 26
operand: 17
15Variable
16ExprTuple17
17Operationoperator: 18
operands: 19
18Literal
19ExprTuple20, 21
20Literal
21Operationoperator: 22
operands: 23
22Literal
23ExprTuple24, 25
24Literal
25Operationoperator: 26
operand: 28
26Literal
27ExprTuple28
28Literal