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Expression of type LessEq

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 m, n
from proveit.numbers import Exp, LessEq, ModAbs, Neg, frac, one, subtract, two
from proveit.physics.quantum.QPE import phase, two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = LessEq(ModAbs(subtract(frac(m, two_pow_t), phase), one), Exp(two, Neg(n)))
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|\frac{m}{2^{t}} - \varphi\right|_{\textup{mod}\thinspace 1} \leq 2^{-n}
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: 5
operands: 6
4Operationoperator: 24
operands: 7
5Literal
6ExprTuple8, 9
7ExprTuple26, 10
8Operationoperator: 11
operands: 12
9Literal
10Operationoperator: 19
operand: 16
11Literal
12ExprTuple14, 15
13ExprTuple16
14Operationoperator: 17
operands: 18
15Operationoperator: 19
operand: 23
16Variable
17Literal
18ExprTuple21, 22
19Literal
20ExprTuple23
21Variable
22Operationoperator: 24
operands: 25
23Variable
24Literal
25ExprTuple26, 27
26Literal
27Variable